07 Jan It appears that justices
Homework 4
1. A newspaper provided a? “snapshot” illustrating poll results from 1910 professionals who interview job applicants. The illustration showed that? 26% of them said the biggest interview turnoff is that the applicant did not make an effort to learn about the job or the company. The margin of error was given as plus or minus 3 percentage points. What important feature of the poll was? omitted?
Choose the correct answer.
The point estimate
The confidence level
The sample size
The confidence interval
2. Find the critical value z Subscript alpha divided by 2 that corresponds to the given confidence level.
96?%
z Subscript alpha divided by 2equals
3. In a poll of 598 human resource? professionals, 46.3?% said that body piercings and tattoos were big grooming red flags. Complete parts? (a) through? (d) below.
?a) Among the 598 human resource professionals who were? surveyed, how many of them said that body piercings and tattoos were big grooming red? flags?
________?(Round to the nearest integer as? needed.)
?b) Construct a? 99% confidence interval estimate of the proportion of all human resource professionals believing that body piercings and tattoos are big grooming red flags.
_______ less than p less than ____________?(Round to three decimal places as? needed.)
?c) Repeat part? (b) using a confidence level of? 80%.______less than p less than______?(Round to three decimal places as? needed.)
?d) Compare the confidence intervals from parts? (b) and? (c) and identify the interval that is wider. Why is it? wider?
Select the correct choice below and fill in the answer boxes to complete your choice.
A.
The
nothing?% confidence interval is wider than the
nothing?% confidence interval. As the confidence interval? narrows, the probability that the confidence interval actually does contain the sample parameter increases.
B.
The
nothing?% confidence interval is wider than the
nothing?% confidence interval. As the confidence interval? widens, the probability that the confidence interval actually does contain the sample parameter increases.
C.
The
nothing?% confidence interval is wider than the
nothing?% confidence interval. As the confidence interval? narrows, the probability that the confidence interval actually does contain the population parameter increases.
D.
The ____confidence interval is wider than the ______confidence interval. As the confidence interval? widens, the probability that the confidence interval actually does contain the population parameter increases.
4. Do one of the? following, as appropriate.? (a) Find the critical value z Subscript alpha divided by 2?, ?(b) find the critical value t Subscript alpha divided by 2?, ?(c) state that neither the normal nor the t distribution applies.
Confidence level 95?%; nequals20?; sigma is known?; population appears to be very skewed.
Find the critical value.
A.
t Subscript alpha divided by 2 Baseline equals 2.093
B.
z Subscript alpha divided by 2equals1.645
C.
z Subscript alpha divided by 2 Baseline equals 1.96
D.
t Subscript alpha divided by 2equals1.729
E.
Neither normal nor t distribution applies.
5. In a test of the effectiveness of garlic for lowering? cholesterol, 44 subjects were treated with garlic in a processed tablet form. Cholesterol levels were measured before and after the treatment. The changes in their levels of LDL cholesterol? (in mg/dL) have a mean of 3.5 and a standard deviation of 17.1. Complete parts? (a) and? (b) below.
a. What is the best point estimate of the population mean net change in LDL cholesterol after the garlic? treatment?
The best point estimate is _______?mg/dL.
?(Type an integer or a? decimal.)
b. Construct a 95?% confidence interval estimate of the mean net change in LDL cholesterol after the garlic treatment. What does the confidence interval suggest about the effectiveness of garlic in reducing LDL? cholesterol?
What is the confidence interval estimate of the population mean mu??
?(Round to two decimal places as? needed.)
What does the confidence interval suggest about the effectiveness of the? treatment?
A.
The confidence interval limits contain ?0, suggesting that the garlic treatment did not affect the LDL cholesterol levels.
B.
The confidence interval limits do not contain ?0, suggesting that the garlic treatment did affect the LDL cholesterol levels.
C.
The confidence interval limits contain ?0, suggesting that the garlic treatment did affect the LDL cholesterol levels.
D.
The confidence interval limits do not contain ?0, suggesting that the garlic treatment did not affect the LDL cholesterol levels.
6. Twelve different video games showing substance use were observed and the duration times of game play? (in seconds) are listed below. The design of the study justifies the assumption that the sample can be treated as a simple random sample. Use the data to construct a 95?% confidence interval estimate of mu?, the mean duration of game play.
4045
3886
3854
4023
4313
4820
4654
4039
5000
4831
4335
4324
What is the confidence interval estimate of the population mean mu??
?(Round to one decimal place as? needed.)
7. An IQ test is designed so that the mean is 100 and the standard deviation is 16 for the population of normal adults. Find the sample size necessary to estimate the mean IQ score of statistics students such that it can be said with 99?% confidence that the sample mean is within 4 IQ points of the true mean. Assume that sigmaequals16 and determine the required sample size using technology. Then determine if this is a reasonable sample size for a real world calculation.
The required sample size is _____?(Round up to the nearest? integer.)
Would it be reasonable to sample this number of? students?
No. This number of IQ test scores is a fairly large number.
Yes. This number of IQ test scores is a fairly large number.
No. This number of IQ test scores is a fairly small number.
Yes. This number of IQ test scores is a fairly small number.
8. If we find that there is a linear correlation between the concentration of carbon dioxide in our atmosphere and the global? temperature, does that indicate that changes in the concentration of carbon dioxide cause changes in the global? temperature?
Choose the correct answer below.
A.
Yes. The presence of a linear correlation between two variables implies that one of the variables is the cause of the other variable.
B.
No. The presence of a linear correlation between two variables does not imply that one of the variables is the cause of the other variable.
9. For a sample of eight? bears, researchers measured the distances around the? bears’ chests and weighed the bears. Minitab was used to find that the value of the linear correlation coefficient is requals0.989. Using alpha = 0.05, determine if there is a linear correlation between chest size and weight. What proportion of the variation in weight can be explained by the linear relationship between weight and chest? size?
a. Is there a linear correlation between chest size and? weight?
A.
?No, because the absolute value of the test statistic exceeds the critical value of 0.707.
B.
?Yes, because the test statistic falls between the critical values of negative 0.707 and 0.707.
C.
?Yes, because the absolute value of the test statistic exceeds the critical value of 0.707.
D.
The answer cannot be determined from the given information.
b. What proportion of the variation in weight can be explained by the linear relationship between weight and chest? size?
?(Round to three decimal places as? needed.)
10. Listed below are amounts of court income and salaries paid to the town justices. All amounts are in thousands of dollars. Construct a? scatterplot, find the value of the linear correlation coefficient? r, and find the? P-value using alphaequals0.05. Is there sufficient evidence to conclude that there is a linear correlation between court incomes and justice? salaries? Based on the? results, does it appear that justices might profit by levying larger? fines?
Court Income
65.0
406.0
1567.0
1131.0
272.0
251.0
111.0
155.0
31.0
Justice Salary
31
44
94
58
46
62
26
27
19
What are the null and alternative? hypotheses?
A.
Upper H 0?: rhoequals0
Upper H 1?: rhonot equals0
.B.
Upper H 0?: rhoequals0
Upper H 1?: rhogreater than0
C.
Upper H 0?: rhoequals0
Upper H 1?: rholess than0
D.
Upper H 0?: rhonot equals0
Upper H 1?: rhoequals0
Construct a scatterplot. Choose the correct graph below.
A.
0
800
1600
0
50
100
Court Income
Justice Salary
A scatterplot has a horizontal scale labeled “Court Income” from 0 to 1600 in intervals of 200 and a vertical scale labeled “Justice Salary” from 0 to 100 in intervals of 10. Nine points are plotted with approximate coordinates as follows: (220, 84); (220, 80); (360, 80); (400, 70); (580, 84); (740, 58); (1080, 62); (1120, 30); (1420, 44).
B.
0
800
1600
0
50
100
Court Income
Justice Salary
A scatterplot has a horizontal scale labeled “Court Income” from 0 to 1600 in intervals of 200 and a vertical scale labeled “Justice Salary” from 0 to 100 in intervals of 10. Nine points are plotted with approximate coordinates as follows: (140, 14); (140, 36); (340, 42); (660, 54); (740, 66); (900, 74); (1280, 90); (1320, 14); (1420, 74).
C.
0
800
1600
0
50
100
Court Income
Justice Salary
A scatterplot has a horizontal scale labeled “Court Income” from 0 to 1600 in intervals of 200 and a vertical scale labeled “Justice Salary” from 0 to 100 in intervals of 10. Nine points are plotted with approximate coordinates as follows: (40, 20); (60, 32); (120, 26); (160, 28); (260, 62); (280, 46); (400, 44); (1140, 58); (1560, 94).
D.
0
800
1600
0
50
100
Court Income
Justice Salary
A scatterplot has a horizontal scale labeled “Court Income” from 0 to 1600 in intervals of 200 and a vertical scale labeled “Justice Salary” from 0 to 100 in intervals of 10. Nine points are plotted with approximate coordinates as follows: (260, 84); (420, 24); (640, 56); (760, 86); (880, 48); (900, 34); (1040, 86); (1260, 46); (1480, 18).
The linear correlation coefficient r is _____?(Round to three decimal places as? needed.)
The test statistic t is ______?(Round to three decimal places as? needed.)
The? P-value is ____?(Round to three decimal places as? needed.)
Because the? P-value is ____than the significance level 0.05?, there _____sufficient evidence to support the claim that there is a linear correlation between court incomes and justice salaries for a significance level of alphaequals0.05.
Based on the? results, does it appear that justices might profit by levying larger? fines?
A.
It appears that justices profit the same despite the amount of the fines.
B.
It does appear that justices might profit by issuing smaller fines.
C.
It does not appear that justices might profit by levying larger fines.
D.
It does appear that justices might profit by levying larger fines.
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