Answer:
The 95% confidence interval for the mean of all body temperatures is between 97.76 ºF and 99.12 ºF
Step-by-step explanation:
We have the standard deviation for the sample, so we use the t-distribution to solve this question.
The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So
df = 10 - 1 = 9
95% confidence interval
Now, we have to find a value of T, which is found looking at the t table, with 9 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.95}{2} = 0.975[/tex]. So we have T = 2.2622
The margin of error is:
M = T*s = 2.2622*0.3 = 0.68
In which s is the standard deviation of the sample.
The lower end of the interval is the sample mean subtracted by M. So it is 98.44 - 0.68 = 97.76 ºF
The upper end of the interval is the sample mean added to M. So it is 98.44 + 0.68 = 99.12 ºF
The 95% confidence interval for the mean of all body temperatures is between 97.76 ºF and 99.12 ºF
Which chart is good for showing the following? For each part, choose the most appropriate chart from the charts listed. - trends over time - cross tabulation - the relationship among 3 quantitative variables - the relationship between 2 quantitative variables - frequency distribution of quantitative data - show differences in numbers across categories A. column or bar chart B. line chart C. heat map D. clustered column or bar chart E. bubble chart F. scatter chart G. histogram
Answer:
Step-by-step explanation:
Trends over time - Line charts
Cross tabulation - column or bar chart
The relationship among 3 quantitative variables - Bubble charts or clusteréd column or bar chart
The relationship between 2 quantitative variables - scatter plot
Frequency distribution of quantitative data - Histogram
Show differences in numbers across categories - Bar chart or column charts.
Your friend believes that he has found a route to work that would make your commute faster than what it currently is under similar conditions. Suppose that data were collected for a random set of 7 days, where each difference is calculated by subtracting the time taken on the current route from the time taken on the new route. Assume that the populations are normally distributed. Your friend uses the alternative hypothesis Ha:μd<0. Suppose the test statistic t is computed as t≈−3.201, which has 6 degrees of freedom. What range contains the p-value?
Answer:
The range of p-values
0.01 < p < 0.025
Step-by-step explanation:
Explanation:-
Given random sample size 'n' = 7
Assume that the populations are normally distributed
Null Hypothesis :H₀:μd=0.
Alternative Hypothesis:H₁:μd<0.
Degrees of freedom
ν = n-1 =7-1 =6
given the test statistic t = - 3.201
we will use single tailed test in t-distribution table
The test statistic t= 3.201 is lies between the critical values is 0.01 and 0.025
The range of p-values
0.01 < p < 0.025 (check t- distribution table single tailed test)
Final answer:-
The range of p-values
0.01 < p < 0.025
A teacher figures that final grades in the chemistry department are distributed as: A, 25%; B, 25%;C, 40%;D, 5%; F, 5%. At the end of a randomly selected semester, the following number of grades were recorded. Calculate the chi-square test statistic x^2 to determine if the grade distribution for the department is different than expected. Use α = 0.01.
Grade A B C D F
Number 36 42 60 14 8
a. 6.87
b. 0.6375
c. 5.25
d. 4.82
Answer:
[tex]E_{A} =0.25*160=40[/tex]
[tex]E_{B} =0.25*160=40[/tex]
[tex]E_{C} =0.4*160=64[/tex]
[tex]E_{D} =0.05*160=8[/tex]
[tex]E_{F} =0.05*160=8[/tex]
And now we can calculate the statistic:
[tex]\chi^2 = \frac{(36-40)^2}{40}+\frac{(42-40)^2}{40}+\frac{(60-64)^2}{64}+\frac{(14-8)^2}{8}+\frac{(8-8)^2}{8} =5.25[/tex]
The answer would be:
c. 5.25
Step-by-step explanation:
The observed values are given by:
A: 36
B: 42
C: 60
D: 14
E: 8
Total =160
We need to conduct a chi square test in order to check the following hypothesis:
H0: There is no difference in the proportions for the final grades
H1: There is a difference in the proportions for the final grades
The level of significance assumed for this case is [tex]\alpha=0.01[/tex]
The statistic to check the hypothesis is given by:
[tex]\chi^2 =\sum_{i=1}^n \frac{(O_i -E_i)^2}{E_i}[/tex]
Now we just need to calculate the expected values with the following formula [tex]E_i = \% * total[/tex]
And the calculations are given by:
[tex]E_{A} =0.25*160=40[/tex]
[tex]E_{B} =0.25*160=40[/tex]
[tex]E_{C} =0.4*160=64[/tex]
[tex]E_{D} =0.05*160=8[/tex]
[tex]E_{F} =0.05*160=8[/tex]
And now we can calculate the statistic:
[tex]\chi^2 = \frac{(36-40)^2}{40}+\frac{(42-40)^2}{40}+\frac{(60-64)^2}{64}+\frac{(14-8)^2}{8}+\frac{(8-8)^2}{8} =5.25[/tex]
The answer would be:
c. 5.25
Now we can calculate the degrees of freedom for the statistic given by:
[tex]df=(categories-1)=(5-1)=4[/tex]
And we can calculate the p value given by:
[tex]p_v = P(\chi^2_{4} >5.25)=0.263[/tex]
The p value is higher than the significance so we have enough evidence to FAIL to reject the null hypothesis
Two airplanes leave an airport at the same time, flying in the same direction. One plane is flying at twice the speed of the other. If after 4 hours they are 1800 km apart, find the speed of each plane.
Answer:
One plane has a speed of 450 km/h and the other has a speed of 900 km/h.
Step-by-step explanation:
I am going to say that:
The speed of the first plane is x.
The speed of the second plane is y.
One plane is flying at twice the speed of the other.
I will say that y = 2x. We could also say that x = 2y.
Two airplanes leave an airport at the same time, flying in the same direction
They fly in the same direction, so their relative speed(difference) at the end of each hour is y - x = 2x - x = x.
If after 4 hours they are 1800 km apart, find the speed of each plane
After 1 hour, they will be x km apart. After 4, 1800. So
1 hour - x km apart
4 hours - 1800 km apart
4x = 1800
x = 1800/4
x = 450
2x = 2*450 = 900
One plane has a speed of 450 km/h and the other has a speed of 900 km/h.
The HCF of two numbers is 11, and their L.C.M is 368. If one number is 64, then the other
number is ….
Find the value of a. a) 15 b) 10 c) 25 d) 20
Answer:
answer d) 20
Step-by-step explanation:
Because the two lines are parallel two by two, the figure is a parallelogram.
In a parallelogram the opposite corners are identical.
Given:
opposite corner1 = 130°
opposite corner2= (6a + 10)°
Because corner1 = corner2 we now have:
(6a + 10) = 130
6a + 0 = 130 -10
6a = 120
a = 20
Which is answer d).
A fair spinner has 11 equal sections: 3 red, 4 blue and 4 green. It is spun twice. What is the probability of getting the same colour twice?
Answer:
The probability of getting the same colour twice is approximately 34%.
Step-by-step explanation:
The probability of getting each color is:
P(x=red) = 3/11 P(x=blue) = 4/11P(x=green) = 4/11Then, we can calculate the probability of getting the color red twice as:
[tex]P(x_1=R;x_2=R)=P(x=R)^2=(3/11)^2=9/121[/tex]
We have to repeat this for the color blue and green:
[tex]P(x_1=B;x_2=B)=P(x=B)^2=(4/11)^2=16/121\\\\P(x_1=G;x_2=G)=P(x=G)^2=(4/11)^2=16/121[/tex]
Then, the probability of getting the same color twice in two spins can be calculated as:
[tex]P=P(x_1=R;x_2=R)+P(x_1=B;x_2=B)+P(x_1=G;x_2=G)=\\\\P=9/121+16/121+16/121\\\\P=41/121\approx0.34[/tex]
There is a clothing store in Bartlesville. The owner has devised his own method of pricing items. A vest costs $20, socks cost $25, a tie costs $15 and a blouse costs $30. Using the method, how much would underwear cost?
Answer:
25
Step-by-step explanation:
I'm going with $25 since socks should cost as much as underwear, you wear them underneath and they're an essential.
what is X:
|4x−1|=3
|x|=−4
Answer:
1
Step-by-step explanation:
If a random sample of 53 students was asked for the number of semester hours they are taking this semester. The sample standard deviation was found to be s = 4.7 semester hours. How many more students should be included in the sample to be 99% sure that the sample mean x is within 1 semester hour of the population mean for all students at this college?
Answer:
94 more students should be included in the sample.
Step-by-step explanation:
We have that to find our [tex]\alpha[/tex] level, that is the subtraction of 1 by the confidence interval divided by 2. So:
[tex]\alpha = \frac{1-0.99}{2} = 0.005[/tex]
Now, we have to find z in the Ztable as such z has a pvalue of [tex]1-\alpha[/tex].
So it is z with a pvalue of [tex]1-0.005 = 0.995[/tex], so [tex]z = 2.575[/tex]
Now, find the margin of error M as such
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
In which [tex]\sigma[/tex] is the standard deviation of the population and n is the size of the sample.
How many students we need to sample to be 99% sure that the sample mean x is within 1 semester hour of the population mean?
We need to survey n students.
n is found when M = 1.
We have that [tex]\sigma = 4.7[/tex]
So
[tex]M = z*\frac{\sigma}{\sqrt{n}}[/tex]
[tex]1 = 2.575*\frac{4.7}{\sqrt{n}}[/tex]
[tex]\sqrt{n} = 2.575*4.7[/tex]
[tex](\sqrt{n})^{2} = (2.575*4.7)^{2}[/tex]
[tex]n = 146.47[/tex]
Rounding up
147 students need to be surveyed.
How many more students should be included...?
53 have already been surveyed
147 - 53 = 94
94 more students should be included in the sample.
Does a point have a one dimension length
Answer:
No.
Step-by-step explanation:
A point has no length, height or depth. It only has position.
A line has one dimensional length.
The mass of the Eiffel Tower is about 9.16 ⋅ 10^6 kilograms. The mass of the Golden Gate Bridge is 8.05 ⋅ 10^8 kilograms. Approximately how many more kilograms is the mass of the Golden Gate Bridge than the mass of the Eiffel Tower? Show your work and write your answer in scientific notation.
Answer:
[tex]7.9584 \times 10^8[/tex]
Step-by-step explanation:
[tex]8.05 \times 10^8 - 9.16 \times 10^6[/tex]
[tex]805000000-9160000[/tex]
[tex]=795840000[/tex]
divide the following polynomials ( 9 x 4 + 3 x 3 y − 5 x 2 y 2 + x y 3 ) ÷ ( 3 x 2 + 2 x 2 y − x y 2 )
Answer:
2(-2y+9)/3+y
Step-by-step explanation:
5. The value of 25sqare -24sqare
Answer:
49
Step-by-step explanation:
25²-24²
625-576
=49
use calculator lah dehh
Which equation can be used to solve for b?
B
5 cm
С
10 cm
b
30
A
O tan(30)=5/b
O tan(30)=b/5
O tan(30)=10/b
O tan(30)=b/10
Answer:
The answer is option 1.
Step-by-step explanation:
You have to apply Tangent Rule, tanθ = opposite/adjacent:
[tex] \tan(θ) = \frac{oppo.}{adj.} [/tex]
[tex]let \: oppo. = 5 \\ let \: adj. = b \\ let \: θ = 30[/tex]
[tex] \tan(30) = \frac{5}{b} [/tex]
The correct answer is option (A) tan(30)=5/b
Tangent functionThe tangent function is one of the main six trigonometric functions and is generally written as tan x. It is the ratio of the opposite side and the adjacent side of the angle in consideration in a right-angled triangle.How to solve this problem?The steps are as follow:
The right angle triangle is given whose sides are as follow:AB = 10 cm
BC = 5 cm
AC = b cm
To find the tan(30) we will use following formula:tan(x) = opposite side / adjacent side
tan(30) = BC / AC
tan(30) = 5 / b
So, the correct answer is option (A) tan(30)=5/b
Learn more about Tangent function here:
https://brainly.com/question/6904750
#SPJ2
Suppose you would like to save P9000 invested at 8% compounded quarterly for 5 years and 6 months. (Note: Round off your answer to the nearest hundredth) (a) How much would the value of her savings at the end of the term? Answer (b) How much is the interest earned by your savings? Answer
Answer:
a) 13913
b) 4913.82
Step-by-step explanation:
The compound interest formula is given by:
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
Where A(t) is the amount of money after t years, P is the principal(the initial sum of money), r is the interest rate(as a decimal value), n is the number of times that interest is compounded per year and t is the time in years for which the money is invested or borrowed.
In this question:
Investment of 9000, so [tex]P = 9000[/tex]
Interest rate of 8%, so [tex]r = 0.08[/tex]
Compounded quarterly, so [tex]n = 4[/tex]
5 years and 6 months, that is, 5 years and half, so [tex]t = 5.5[/tex]
(a) How much would the value of her savings at the end of the term?
[tex]A(t) = P(1 + \frac{r}{n})^{nt}[/tex]
[tex]A(5.5) = 9000(1 + \frac{0.08}{4})^{4*5.5} = 13913.82[/tex]
(b) How much is the interest earned by your savings?
The amount subtracted by the principal. So
13913.82 - 9000 = 4913.82
Assume that women's heights are normally distributed with a mean of 63.6 inches and a standard deviation of 2.5 inches. If 90 women are randomly selected, find the probability that they have a mean height between 62.9 inches and 64.0 inches.
A. 0.7248
B. 0.0424
C. 0.1739
D. 0.9318
The lines shown below are perpendicular if the green line has a slope of 3/4 what is the slopes of the red line?
Answer:
b) -4/3
Step-by-step explanation:
perpendicular lines have slopes that are opposite reciprocals. the opposite of 3/4 is -3/4, and the reciprocal of -3/4 is -4/3. hope this helps!
Answer:
It is -4/3
Step-by-step explanation:
A random sample of 100 observations from a population with standard deviation 6868 yielded a sample mean of 113113. Complete parts a through c below. a. Test the null hypothesis that muμequals=100 against the alternative hypothesis that muμgreater than>100, using alphaαequals=0.05. Interpret the results of the test. What is the value of the test statistic?
Answer:
Null hypothesis is rejected,
test statistic= 15.76
Step-by-step explanation:
sample mean= 113,
sample standard deviation= 68
H0: mean of sample =100
Ha: mean of sample > 100
test statistic= (population mean- sample mean)/√(standard deviation/sample size)
test statistic= (113-100)/√(68/100)= 15.76
Degrees of freeedom= 100-1=99
p-value= 1.658 (from t distribution table for DF=99 and alpha=0.05)
Since p-value is smaller than test statistic, null hypothesis is rejected
1. If the ratio of the ages of Kissi and Esinam is 3:5 and that of Esinam and Lariba is 3:5 and
the sum of the ages of all 3 is 147 years, what is the age difference between oldest the
youngest?
Ans: years
2. The HCF of two numbers is 11, and their L.C.M is 368. If one number is 64, then the other
number is ….
Answer:
1) 48 years.
2) Question incorrect.
11 isn't a factor of 64, and 368 isn't a multiple of 64. 11 also isn't a factor of 368, hence, it would be impossible to find the unknown second number with all of these false information in the question.
Step-by-step explanation:
Let the ages of Kissi, Esinam and Lariba be x, y and z respectively.
Ratio of the ages of Kissi and Esinam is 3:5
x:y = 3:5
(x/y) = (3/5)
5x = 3y
x = (3y/5) (eqn 1)
Ratio of the ages of Esinam and Lariba is 3:5
y:z = 3:5
(y/z) = (3/5)
5y = 3z
z = (5y/3) (eqn 2)
The sum of their 3 ages is 147
x + y + z = 147 (eqn 3)
Substituting the values of x and z from eqn 1 and 2 into eqn 3, we have
(3y/5) + y + (5y/3) = 147
(49y/15) = 147
y = (147×15/49) = 45.
x = (3y/5) = (3×45/5) = 27
z = (5y/3) = (5×45/3) = 75
The ages of Kissi, Esinam and Lariba are then 27, 45 and 75 respectively.
The difference in the ages of the oldest amf the youngest is thus, 75 - 27 = 48 years.
2) This question seems to be faulty and incorrect as 11 isn't a factor of 64, and 368 isn't a multiple of 64. 11 also isn't a factor of 368, hence, it would be impossible to find the unknown second number with all of these false information in the question.
Hope this Helps!!!
An urban economist is curious if the distribution in where Oregon residents live is different today than it was in 1990. She observes that today there are approximately 3,109 thousand residents in NW Oregon, 902 thousand residents in SW Oregon, 244 thousand in Central Oregon, and 102 thousand in Eastern Oregon. She knows that in 1990 the breakdown was as follows:
72.7% NW Oregon, 20.7% SW Oregon, 4.8% Central Oregon, and 2.8% Eastern Oregon.
Can she conclude that the distribution in residence is different today at a 0.05 level of significance?
a) Yes, because the p-value = .0009.
b) No, because the p-value = .0009.
c) Yes, because the p-value = .0172.
d) No, because the p-value = .0172.
Answer:
c) Yes, because the p-value = 0.0172
Step-by-step explanation:
The following table is obtained:
Categories Observed(fo) Expected (fe) (fo-fe)²/fe
NW Oregon 3109 4357*0.727=3167.539 1.082
SW Oregon 902 4357*0.207=901.899 0
Central Oregon 244 4357*0.048=209.136 5.812
Eastern Oregon 102 4357*0.028=121.996 3.277
Sum = 4357 4357 10.171
(1) Null and Alternative Hypotheses
The following null and alternative hypotheses need to be tested:
H0:p1=0.727,p2=0.207,p3=0.048,p4=0.028
Ha: Some of the population proportions differ from the values stated in the null hypothesis
This corresponds to a Chi-Square test for Goodness of Fit.
(2) Rejection Region
Based on the information provided, the significance level is α=0.05, the number of degrees of freedom is df=4−1=3, so then the rejection region for this test is R={χ2:χ2>7.815}.
(3) Test Statistics
The Chi-Squared statistic is computed as follows:
[tex]X^2=\sum^n_{i=1}\frac{(O_i-E_i)^2}{y} \\\\= 1.082+0+5.812 +3.277 = 10.171[/tex]
(4) Decision about the null hypothesis
Since it is observed that
[tex]X^2 = 10.171 > X_c^2 = 7.815[/tex]
it is then concluded that the null hypothesis is rejected.
(5) Conclusion
It is concluded that the null hypothesis H_o is rejected. Therefore, there is enough evidence to claim that some of the population proportions differ from those stated in the null hypothesis, at the α=0.05 significance level.
If the probability of a machine producing a defective part is 0.05, what is the probability of
finding exactly 5 defective parts from a sample of 100? (Assume that the process follows a
binomial distribution and round answer to four places)
Answer:
0.1800 to 4 places of decimals.
Step-by-step explanation:
Using the Binomial formula
Probability = 10C5* (0.95)^95 * (0.05)^5
= 100! / 95!*5! * (0.95)^95 * (0.05)^5
= 0.1800178.
find the slope of the line (-5,2) and (4,2)
Answer:
The answer is 0
Step-by-step explanation:
The number of pieces of popcorn in a large movie theatre popcorn bucket is normally distributed, with a mean of 1610 and a standard deviation of 10. Approximately what percentage of buckets contain between 1600 and 1620 pieces of popcorn?
Answer:
A
Step-by-step explanation:
We know that in normal distribution, approximately 34% of bags will fall with in one standard deviation on one side. On both sides within the range of 1 standard deviation, 34 + 34 = 68 % of bags will fall.
Our range is:
1600 to 1620
1610 - 10 to 1610 + 10
So the answer is 1
That means, that 68% is the answer.
Answer:
The answer is A.
Step-by-step explanation:
Approximately 68%
help asap, will get branliest !!
Answer:
D
Step-by-step explanation:
Lines EF and GH are already parallel. Translating them 2 units to the side without changing how far apart they are vertically means they won't intersect and will remain the same distance apart.
Answer:
D
Step-by-step explanation:
They are parallel lines
Choose the equation for the graph
below.
a. y =
1
X-2
2
b.y =
x²–4
3
c. y =
x+2
-3
d.y=
e. y =
2x+4
1
x2+2x+1
Answer:
C
Step-by-step explanation:
Plugged into calculator
Vertical asymptotes: x=-2
Horizontal asymptotes: y=0
No oblique asymptotes
What is the value of log625^5 converted to a fraction
Answer:
1/4
Step-by-step explanation:
625^x = 5
x = 1/4
please help :( really need answer
Answer:
Options (C) and (F)
Step-by-step explanation:
Polynomial function is,
f(x) = x³ - x² - 5x - 3
Possible rational roots of the given function will be = [tex]\frac{\pm1, \pm3}{\pm1}[/tex]
By putting x = -1
f(-1) = (-1)³ - (-1)² -5(-1) - 3
= -1 - 1 + 5 - 3
= 0
Therefore, x = -1 will a root of the given function.
Now we apply synthetic division to get the other roots,
-1 | 1 -1 -5 -3
↓ -1 2 3
1 -2 -3 0
Therefore, factored form of the polynomial will be (x + 1)(x² - 2x - 3).
Now we will find the roots of (x² -2x - 3).
x² - 2x - 3 = x² - 3x + x - 3
= x(x - 3) + 1(x - 3)
= (x + 1)(x - 3)
For roots of the function, f(x) = 0
(x + 1)(x - 3) = 0
x = -1, 3
Therefore, roots of the function are x = -1, 3
Options (C) and (F) are the answers.
The table below represents the total cost of leasing a car at the end each month.
Month 1 -------- 3 -------- 8 -------- 12
Cost $1,859 --- $2,577 --- $4,372 --- $5,808
Write an equation in slope-intercept form to represent the total cost, y, of leasing a car for x months.
Answer:
y= 359 x+1500
Step-by-step explanation:
find the slope m= (2577-1859)÷(3-1) = 359
y=mx+b
find b : substitute x ,y, and m
get b = 1857 - 359*1 = 1500
Answer:
y= 359 x+1500
Step-by-step explanation:
Suppose your total taxable income this year is $75,000 you are taxed a rate of 10 percent on the first 25,000 20 percent on the next 25,000 and 30 percent on the final 25,000 what is your total income tax