E270 Final Exam Solution

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The right way to think about the sample mean is:

The sample mean is a constant number.

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

The sample mean is always close to the population mean.

The sample mean is always smaller than the population mean.

The sampling distribution of x̅ is approximately normal if

the distribution of x is skewed.

the distribution of x is approximately symmetric

the sample size is large enough.

the sample size is small enough.

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 _____.

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 (x̅) will be within ±3 cars from the population mean is _________.

0.9876

0.9544

0.9266

0.8664

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(p̅), is _______.

0.38

0.28

0.25

0.18

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

0.0343

0.0297

0.0248

0.0221

The expression

Means:

Once you take a specific sample and calculate the value of x̅, the probability that the value of x̅ you just calculated is within ±1.96 σ/√n from μ is 0.95.

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

Once you take a specific sample and calculate the value of x̅, you are 95 percent certain that the value you calculated is μ.

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

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.

480

456

400

380

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

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 x̅ = 250 with a sample standard deviation of s = 36 customers. The 95 percent confidence interval for the mean daily customer visits is:

(205, 295)

(217, 283)

(222, 278)

(226, 274)

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.

101

139

200

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:

is wider.

is narrower.

has the same precision.

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

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:

(0.798, 0.802)

(0.784, 0.816)

(0.771, 0.829)

(0.760, 0.840)

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,

(0.401, 0.499)

(0.410, 0.490)

(0.421, 0.479)

(0.426, 0.474)

John is the manager of an election campaign. John’s 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?

9,604

8,888

5,037

1,499

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.

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

Type I: Reject a true alternative hypothesis.

Type II: Do not reject a false alternative hypothesis.

Type I: Do not Reject a false null hypothesis.

Type II: Reject a true null hypothesis.

Type I: Reject a false null hypothesis.

Type II: Reject a true null hypothesis.

Type I: Reject a true null hypothesis.

Type II: Do not reject a false null hypothesis.

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 ______

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

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

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

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

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 x̅ = 42 years, with a sample standard deviation of s = 18 years. She wants to conduct the test of H₀: μ ≤ 40 with a 5% level of significance. She should reject H₀ if the value of the test statistic is _____

less than the critical value.

greater than the critical value.

more than two standard errors above the critical value.

equal to the critical value.

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

1.49 and does not reject H₀. She concludes that the average age is not over 40.

1.49 and rejects H₀. She concludes that the average age is over 40.

1.74 and does not reject H₀. She concludes that the average age is not over 40.

1.74 and rejects H₀. She concludes that the average age is over 40.

The probability value for Linda’s hypothesis test is ______.

0.0207

0.0409

0.0542

0.0681

The Census Bureau’s 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:

0.039

0.032

0.025

0.020

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

0.0026

0.0071

0.0142

0.0224

Given the following sample data, is there enough evidence, at the 5 percent significance level, the population mean is greater than 7?

Compute the relevant test statistic.

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.

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.

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.

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

ANOVA

Significance F

Regression

27.24937

5.78E-05

Residual

13960.49

Total

35094.63

Coefficients

Std Error

t Stat

P-value

Lower 95%

Upper 95%

Intercept

15.8479

25.0665

0.632

0.5352

-36.815

68.511

Size (Square Feet)

0.0695

0.0133

5.79E-05

0.0416

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

$148.70

$154.80

$159.50

$164.30

The sum of squares regression (SSR) is:

49055.12

35094.63

21134.14

13960.49

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%

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

30.634

33.698

27.849

24.067

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

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E270 Final Exam Solution

E270 Final Exam

The right way to think about the sample mean is

Final Exam of E270