# The right way to think about the sample mean is

The right way to think about the sample mean is:

a The sample mean is a constant number.

b The sample mean is a different value in each random sample from the population mean.

c The sample mean is always close to the population mean.

d The sample mean is always smaller than the population mean.

2

The sampling distribution of x ̅ is approximately normal if

a the distribution of x is skewed.

b the distribution of x is approximately symmetric

c the sample size is large enough.

d the sample size is small enough.

3

a

b

c

d

There is a population of six families in a small neighborhood: Albertson, Benson, Carlson,

Davidson, Erikson, and Fredrickson. You plan to take a random sample of n=3 families (without

replacement). The total number of possible sample is _____.

6

12

18

20

a

b

c

d

The mean daily output of an automobile manufacturing plant is μ = 520 cars with standard

deviation of σ = 14 cars. In a random sample of n = 49 days, the probability that the sample

mean output of cars (x ) will be within ±3 cars from the population mean is _________.

̅

0.9876

0.9544

0.9266

0.8664

a

b

c

d

In the population of IUPUI undergraduate students 38 percent (0.38) enroll in classes during the

summer sessions. Let p̅ denote the sample proportion of students who plan to enroll in summer

classes in samples of size n = 200 selected from this population. The expected value of the

sample proportion, E(p), is _______.

̅

0.38

0.28

0.25

0.18

a

b

c

d

In the previous question, the standard error of the sampling distribution of p ̅ is, se(p)=_______.

̅

0.0343

0.0297

0.0248

0.0221

4

5

6

7

The expression

Means:

a Once you take a specific sample and calculate the value of x, the probability that the value of x ̅

̅

you just calculated is within ±1.96 σ/n from μ is 0.95.

b In repeated samples, the probability that x ̅ is within ±1.96 σ/n from μ is 0.95.

c Once you take a specific sample and calculate the value of x, you are 95 percent certain that the

̅

value you calculated is μ.

d In repeated samples, you are 95 percent certain that the value of x ̅ is μ.

8

As part of a course assignment to develop an interval estimate for the proportion of IUPUI

students who smoke tobacco, each of 480 E270 students collects his or her own random sample

of n=400 IUPUI students to construct a 95 percent confidence interval. Considering the 480

intervals constructed by the E270 students, we would expect ________ of these intervals to

capture the population proportion of IUPUI students who smoke tobacco.

a

480

b

456

c

400

d

380

9

a

b

c

d

Assume the actual population proportion of IUPUI students who smoke tobacco is 20 percent

(0.20). What proportion of sample proportions obtained from random samples of size n=300 are

within a margin of error of ±3 percentage points (±0.03) from the population proportion?

0.8064

0.8472

0.8858

0.9050

10

To estimate the average number of customers per business day visiting a branch of Fifth National

Bank, in a random sample of n = 9 business days the sample mean number of daily customer

visits is x ̅ = 250 with a sample standard deviation of s = 36 customers. The 95 percent

confidence interval for the mean daily customer visits is:

a (205, 295)

b (217, 283)

c (222, 278)

d (226, 274)

11

a

b

c

d

In the previous question, how large a sample should be selected in order to have a margin of error

of ±5 daily customer visits? Use the standard deviation in that question as the planning value.

78

101

139

200

12

Compared to a confidence interval with a 90 percent confidence level, an interval based on the

same sample size with a 99 percent level of confidence:

a is wider.

b is narrower.

c has the same precision.

d would be narrower if the sample size is less than 30 and wider if the sample size is at least 30.

13

It is estimated that 80% of Americans go out to eat at least once per week, with a margin of error

of 0.04 and a 95% confidence level. A 95% confidence interval for the population proportion of

Americans who go out to eat once per week or more is:

a (0.798, 0.802)

b (0.784, 0.816)

c (0.771, 0.829)

d (0.760, 0.840)

14

In a random sample of 600 registered voters, 45 percent said they vote Republican. The 95%

confidence interval for proportion of all registered voters who vote Republican is,

a (0.401, 0.499)

b (0.410, 0.490)

c (0.421, 0.479)

d (0.426, 0.474)

John is the manager of an election campaign. Johns candidate wants to know what proportion of

the population will vote for her. The candidate wants to know this with a margin of error of ±

0.01 (at 95% confidence). John thinks that the population proportion of voters who will vote for

his candidate is 0.50 (use this for a planning value). How big of a sample of voters should you

take?

a

9,604

b

8,888

c

5,037

d

1,499

15

16

a

b

c

d

If the candidate changes her mind and now wants a margin-of-error of ± 0.03 (but still 95% confidence),

John could select a different sample of the same size, but adjust the error probability.

John should select a larger sample.

John should select a smaller sample.

John should inform the candidate that margin of error does not impact the sample size.

17

In a test of hypothesis, which of the following statements about a Type I error and a Type II error

is correct:

a Type I: Reject a true alternative hypothesis.

Type II: Do not reject a false alternative hypothesis.

b Type I: Do not Reject a false null hypothesis. II: Reject a true null hypothesis.

Type

c Type I: Reject a false null hypothesis.

Type II: Reject a true null hypothesis.

d Type I: Reject a true null hypothesis.

Type II: Do not reject a false null hypothesis.

18

You are reading a report that contains a hypothesis test you are interested in. The writer of the

report writes that the p-value for the test you are interested in is 0.0831, but does not tell you the

value of the test statistic. Using α as the level of significance, from this information you ______

a decide to reject the hypothesis at α = 0.10, but not reject at α = 0.05.

b cannot decide based on this limited information. You need to know the value of the test statistic.

c decide not to reject the hypothesis at α = 0.10, and not to reject at α = 0.05

d decide to reject the hypothesis at α = 0.10, and reject at α = 0.05

19

Linda works for a charitable organization and she wants to see whether the people who donate to

her organization have an average age over 40 years. She obtains a random sample of n = 180

donors and the value of the sample mean is x ̅ = 42 years, with a sample standard deviation of s =

18 years. She wants to conduct the test of H: μ 40 with a 5% level of significance. She

should reject H if the value of the test statistic is _____

a less than the critical value.

b greater than the critical value.

c more than two standard errors above the critical value.

d equal to the critical value.

20 Now she performs the test and obtains the test statistic of TS = ______,

a 1.49 and does not reject H . She concludes that the average age is not over 40.

b 1.49 and rejects H . She concludes that the average age is over 40.

c 1.74 and does not reject H . She concludes that the average age is not over 40.

d 1.74 and rejects H . She concludes that the average age is over 40.

21 The probability value for Lindas hypothesis test is ______.

a

0.0207

b

0.0409

c

0.0542

d

0.0681

The Census Bureaus American Housing Survey has reported that 80 percent of families choose

their house location based on the school district. To perform a test, with a probability of Type I

error of 5 percent, that the population proportion really equals 0.80, in a sample of 600 families

504 said that they chose their house based on the school district. The null hypothesis would be

rejected if the sample proportion falls outside the margin of error. The margin of error for the test

is:

a

0.039

b

0.032

c

0.025

d

0.020

22

23 The probability value for the hypothesis test in the previous question is:

a

0.0026

b

0.0071

c

0.0142

d

0.0224

24

Given the following sample data, is there enough evidence, at the 5 percent significance level, the

population mean is greater than 7?

x

9

2

15

17

8

11

13

5

Compute the relevant test statistic.

a The test statistic is 1.683 and the critical value is 1.895. Do not reject the null hypothesis and

conclude that the population mean is not greater than 7.

b The test statistic is 1.683 and the critical value is 1.895. Reject the null hypothesis and conclude

that the population mean is greater than 7.

c The test statistic is 2.432 and the critical value is 2.365. Reject the null hypothesis and conclude

that the population mean is greater than 7.

d The test statistic is 2.432 and the critical value is 1.895. Reject the null hypothesis and conclude

that the population mean is not greater than 7.

Next SIX questions are based on the following regression model

In a regression model relating the price of homes (in $1,000) as the dependent variable to their

size in square feet, a sample of 20 homes provided the following regression output. Some of the

calculations are left blank for you to compute.

SUMMARY OUTPUT

Regression Statistics

Multiple R

0.7760

R Square

Adjusted R Square

0.5801

Standard Error

Observations

20

ANOVA

Regression

Residual

Total

df

SS

1

18 13960.49

19 35094.63

Coefficients Std Error

Intercept 15.8479 25.0665

Size (Square Feet)

0.0695

0.0133

MS

F Significance F

27.2494 5.78E-05

t Stat

P-value Lower 95% Upper 95%

0.632

0.5352 -36.815

68.511

5.79E-05

0.0416

25 The model predicts that the price of a home with a size of 2,000 square feet would be ______ thousand.

a

$148.70

b $154.80

c

$159.50

d $164.30

26 The sum of squares regression (SSR) is:

a 49055.12

b 35094.63

c 21134.14

d 13960.49

27

a

b

c

d

The regression model estimates that _____% of the variation in the price of the home is explained

by the size of the homes.

60.20%

65.60%

71.50%

77.20%

28 The standard error of the regression (standard error of estimate) is ______.

a

30.634

b

33.698

c

27.849

d

24.067

29

a

b

c

d

30

a

b

c

d

The value of the test statistic to test the null hypothesis that property size does not influence the

price of the property is ______.

4.348

5.226

6.391

6.982

The margin of error to build a 95% confidence interval for the slope coefficient that relates the

price response to each additional square foot is _______.

0.042

0.032

0.034

0.028