8.3 Quiz

Bags of a certain brand of tortilla chips claim to have a net weight of 14 ounces. A representative of a consumer advocate group wishes to see if there is any evidence that the mean net weight is less than advertised and plans to construct a 95% confidence interval for the mean, using an SRS of 16 bags. Suppose he is not sure if the distribution of net weights is Normal. In which of the following circumstances would he not be safe to use a t procedure because the distribution would not be approximately Normal?

• The sample standard deviation is large.

• The mean and median of the data are nearly equal.

• A stemplot of the data has a large outlier.

• A histogram of the data shows moderate skewness.

• None of these circumstances would prevent the distribution form being approximately Normal.

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.4

CCSS.HSS.ID.A.2

CCSS.HSS.ID.A.3

CCSS.HSS.ID.A.4

The heights (in inches) of males in the United States are believed to be Normally distributed with mean m. The average height of a random sample of twenty-five American adult males is found to be 69.72 inches and the standard deviation of the twenty-five heights is found to be 4.15. The standard error is

• 4.15

• 1.856

• 0.69

• 0.17

• 0.83

What is the critical value t* for a 99% confidence interval when n = 20?

• 2.086

• 2.845

• 2.861

• 2.576

• 2.093

Scores on the SAT Mathematics test (SAT-M) are believed to be Normally distributed with mean m. The scores of a random sample of three students who recently took the exam are 550, 620, and 480. A 95% confidence interval for m based on these data is

•  $550\ \pm\ 1.645\ \times\frac{70}{\sqrt{3}}$  

•  $550\ \pm\ 3.182\ \times\frac{70}{\sqrt{3}}$  

•  $550\ \pm\ 4.303\ \times\ \frac{70}{\sqrt{3}}$  

•  $550\ \pm\ 1.96\ \times\ \frac{70}{\sqrt{3}}$  

• not trustworthy because the conditions for this inference procedure have not been met.

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.4

CCSS.HSS.ID.A.4

A corporation with several thousand employees wants to estimate the mean commute time for all employees. They would like to construct a 95% confidence interval with a margin of error of no more than 4 minutes. Preliminary interviews with a small sample suggest that a reasonable estimate of the population standard deviation is Sx = 10 minutes. Which of the following is the smallest sample the company can take to achieve the desired margin or error?

• 24

• 41

• 25

• 42

• 5

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.4

To estimate a 99% confidence interval for m, the mean salary of full professors at a small community college, you obtain the salaries of a random sample of 30 full professors. The sample mean is and the sample standard deviation is Sx = $4400. Which of the conditions are NOT met?

• The population is not Normally distributed.

• All of the conditions are met.

• The sample size is not greater than or equal to 30

• The sample is not random.

• The population size is not greater than the sample size times 10.

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.3

CCSS.HSS.IC.B.4

CCSS.HSS.ID.A.4

An SRS of 100 postal employees found that the average time these employees had worked for the postal service was 7 years with standard deviation of 2 years. Assume the distribution of the time the population of employees have worked for the postal service is approximately Normal. A 95% confidence interval for the mean time m the population of postal service employees have spent with the postal service is

•  $7\ \pm\ 1.96\ \times\ \frac{2}{\sqrt{100}}$  

•  $7\ \pm\ 1.984\ \times\ \frac{2}{\sqrt{100}}$  

•  $7\ \pm\ 1.990\ \times\ \frac{2}{\sqrt{100}}$  

•  $7\ \pm\ 1.645\ \times\ \frac{2}{\sqrt{100}}$  

• not trustworthy because the conditions for this inference procedure have not been met.

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.4

Suppose we want a 90% confidence interval for the average amount spent on books by freshmen in their first year at a major university. The interval is to have a margin of error of no more than $2, and the amount spent has an approximately Normal distribution with a standard deviation Sx = $30. The number of observations required is closest to

• 30

• 568

• 865

• 25

• 609

Tags

CCSS.HSS.IC.B.4

Twenty-five seniors from a large metropolitan area school district volunteer to allow their Math SAT test scores to be used in a study. These twenty-five seniors had a mean Math SAT score of 450. Suppose we know that the standard deviation of the sample of Math SAT is 100. Assuming that the population of Math SAT scores for seniors in the district is approximately Normally distributed, a 90% confidence interval for the mean Math SAT score m for the population of seniors computed from these data is
A. 450 ± 1.711 ·
B. 450 ± 1.708 ·

•  $450\ \pm\ 1.711\ \times\ \frac{100}{\sqrt{25}}$  

•  $450\ \pm\ 1.708\ \times\ \frac{100}{\sqrt{25}}$  

•  $450\ \pm\ 1.645\ \times\ \frac{100}{\sqrt{25}}$  

•  $450\ \pm\ 1.28\ \times\ \frac{100}{\sqrt{25}}$  

• not trustworthy because the conditions for this inference procedure have not been met.

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.4

CCSS.HSS.ID.A.4

To estimate m, the mean salary of full professors at American colleges and universities, you obtain the salaries of a random sample of 400 full professors. The sample mean is and the sample standard deviation is Sx = $4400. A 99% confidence interval for m is

•  $73,220\ \pm\ 2.626\ \times\ \frac{4400}{\sqrt{400}}$  

•  $73,220\ \pm\ 2.581\ \times\ \frac{4400}{\sqrt{400}}$  

•  $73,220\ \pm\ 2.575\ \times\ \frac{4400}{\sqrt{400}}$  

•  $73,220\ \pm\ 2.33\ \times\ \frac{4400}{\sqrt{400}}$  

• not trustworthy because the conditions for this inference procedure have not been met.

Tags

CCSS.HSS.IC.A.1

CCSS.HSS.IC.B.4

CCSS.HSS.ID.A.4