# compute and choose answer

*label*Statistics

*timer*Asked: May 7th, 2015

**Question description**

Suppose we want to build an interval estimate for the

proportion of Indiana households who live in owneroccupied houses with a 95% confidence level and a margin

of error of ±0.02 (two percentage points). What is the

minimum sample size to achieve this margin of error? Use

0.70 for the planning value.

a) 1537

b) 1801

c) 2017

d) 2401

16) We can make a confidence interval more precise (narrower)

by,

a) increasing the sample size.

b) reducing the confidence level.

c) increasing the confidence level.

d) both (a) and (b) are correct.

17) An interval estimate for the mean weekly wage of Illinois

workers had a lower and upper end, respectively of $1,055

and $1,153. The sample size was n = 196, with a standard

deviation of $294. What is the confidence level for this

interval estimate?

a) 99 percent

b) 98 percent

c) 95 percent

d) 90 percent

18) You read a news report that the average annual textbook

expense for undergraduate students is at least $650. You

want to test the hypothesis that the average for IUPUI

students is at least $650. You select a random sample of 121

students. The sample mean is x̅ = 622, with a sample

standard deviation of $209. Which of the following is the

correct statement of the null and alternative hypotheses?

a) H₀ : µ ≥ 650 H₁ : µ < 650

b) H₀ : µ > 650 H₁ : µ ≤ 650

c) H₀ : µ ≤ 650 H₁ : µ > 650

d) H₀ : µ < 650 H₁ : µ ≥ 650

19) Regardless how you answered the previous question, which

of the following statements is correct?

a) If the mean cost of text books is in fact less than $650

and the hypothesis test leads to reject the null

hypothesis, the you have committed a Type I error.

b) If the mean cost of text books is in fact greater than

$650 and you do not reject the null hypothesis, the you

have committed a Type I error.

c) If the mean cost of text books is in fact less than $650

and you reject the null hypothesis, the you have

committed a Type II error.

d) If the mean cost of text books is in fact less than $650

and you do not reject the null hypothesis, then you have

committed a Type II error.

20) To perform the hypothesis test for the previous question, at

a 5% level of significance, compute the test statistic and the

probability value (p-value). The p-value for the test is,

a) 0.071. Do not reject H₀. Conclude the mea n is no

greater than $650.

b) 0.045. Reject H₀. Conclude the mean is less than $650.

c) 0.071. Do not reject H₀. Conclude the mean is at least

$650.

d) 0.045. Reject H₀. Conclude the mean is greater than

$650.

21) To test if the average fill of half-gallon milk containers is 32

ounces, a random sample of 5 containers were selected,

which yielded the following data.

x

32.0 ∑x = 165

33.0

34.0 ∑x² = 5448.28

32.2

33.8

Compute the test statistic and the critical value at a 5 percent

level of significance. Round both the sample standard

deviation and the standard error to three decimal points.

a) TS = 2.47 ; CV = 2.776. Conclude the mean is equal to 32.

b) TS = 2.47 ; CV = 2.776. Conclude the mean is not equal

to 32.

c) TS = 2.98 ; CV = 2.757. Conclude the mean is equal to 32.

d) TS = 2.47 ; CV = 1.960. Conclude the mean is greater

than 32.

22) You are reading a report that con