BSTAT Test 2 Practice Questions

The Department of Education would like to test the hypothesis that the average debt load of graduating students with a bachelor's degree is equal to $17,000. A random sample of 34 students had an average debt load of $18,200. It is believed that the population standard deviation for student debt load is $4,200. The α is set to 0.05. The p-value for this hypothesis test would be ______.

0.0957

The probability P(Z < 1.28) is closest to ______.

0.90

Find the probability P(−1.90 ≤ Z ≤ 1.90)

0.9426

Suppose that, on average, electricians earn approximately µ = $54,000 per year in the United States. Assume that the distribution for electricians' yearly earnings is normally distributed and that the standard deviation is σ = $12,000. Given a sample of nine electricians, what is the standard deviation for the sampling distribution of the sample mean?

4,000

Statisticians like precision in their interval estimates. A low margin of error is needed to achieve this. Which of the following supports this when selecting sample sizes?

A larger sample size reduces the margin of error.

The standard normal distribution is a normal distribution with a mean equal to zero and a standard deviation equal to ten.

False

The value 0.75 of a sample correlation coefficient indicates a stronger linear relationship than that of -0.90.

False

If a population is known to be normally distributed, what can be said of the sampling distribution of the sample mean drawn from this population?

For any sample size n, the sampling distribution of the sample mean is normally distributed.

If X has a normal distribution with µ = 100 and σ = 5, then the probability P(90 ≤ X ≤ 95) can be expressed in terms of a standard normal variable Z as ______.

P(-2 ≤ Z ≤ -1)

It is known that the length of a certain product X is normally distributed with μ = 20 inches. How is the probability P(X > 16) related to P(X < 16)?

P(X > 16) is greater than P(X < 16).

Assume the sample space S = {win, loss}. Select the choice that fulfills the requirements of the definition of probability.

P({win}) = 0.7, P({loss}) = 0.2

The main ingredient for developing a confidence interval is the sampling distribution of the underlying statistic.

True

A sample regression equation is given by = −100 + 0.5x. If x = 20, the value of y is ________.

Unknown

We draw a random sample of size 25 from the normal population with variance 2.4. If the sample mean is 12.5, what is a 99% confidence interval for the population mean?

[11.7019, 13.2981]

A basketball coach wants to know how many free throws an NBA player shoots during the course of an average practice. The coach takes a random sample of 43 players and finds the average number of free throws shot per practice was 225 with a standard deviation of 35. Construct a 99% confidence interval for the average number of free throws in practice.

[210.5992, 239.4008]

The owner of a large car dealership believes that the financial crisis decreased the number of customers visiting her dealership. The dealership has historically had 800 customers per day. The owner takes a sample of 100 days and finds the average number of customers visiting the dealership per day was 750. Assume that the population standard deviation is 350. At the 5% significance level, the decision is to ___________.

do not reject Ho; we cannot conclude that the mean number of customers visiting the dealership is significantly less than 800

If the p-value for a hypothesis test is 0.07 and the chosen level of significance is α = 0.05, then the correct conclusion is to ____________________.

not reject the null hypothesis

What is the relationship between the standard deviation of the sample mean and the population standard deviation?

se(X) = o/√n

The following scatterplot indicates that the relationship between the two variables x and y is ________.

strong and negative

The following scatterplot indicates that the relationship between the two variables x and y is ________.

strong and positive

The correlation coefficient can only range between 0 and 1.

False

The covariance and correlation coefficient are measures that quantify the non-linear relationship between two variables.

False

The covariance can be use to determine the strength of a linear relationship between two variables.

False

Find the z value such that P(Z ≤ z) = 0.9082.

z = 1.33

If the random variable X is normally distributed with a mean of 55 and a standard deviation of 4, then P(X >55) is:

0.5

The deterministic component of a linear regression model is due to the omission of relevant factors that influence the response variable.

False

The sample correlation coefficient cannot equal zero.

False

Alison has all her money invested in two mutual funds, A and B. She knows that there is a 40% chance that fund A will rise in price, and a 60% chance that fund B will rise in price given that fund A rises in price. What is the probability that both fund A and fund B will rise in price?

0.24

Consider the following hypotheses: H0: p ≥ 0.38 HA: p < 0.38 Compute the p-value based on the following sample information. x = 110; n = 300

0.3192

Two hundred people were asked if they had read a book in the last month. The accompanying contingency table, cross-classified by age, is produced. Under 30 30+ Yes 76 65 No 24 35 The probability that a respondent is at least 30 years old is the closest to ______.

0.33

Find the probability P(−1.96 ≤ Z ≤ 0).

0.4750

What is ...... for a 95% confidence interval of the population mean based on a sample of 15 observations?

2.145

Given an experiment in which a fair coin is tossed three times, the sample space is S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT}. Event A is defined as tossing one head (H). What is the event Ac and what is the probability of this event?

Ac = {TTT, HHT, HTH, THH, HHH}; P(Ac) = 0.625

A 99% confidence interval for the population mean yields the following results: [−3.79, 5.86]. At the 1% significance level, what decision should be made regarding the following hypothesis test with Ho:μ = 0,HA:μ ≠ 0?

Do not reject Ho; we cannot conclude that the mean differs from zero.

A residual is the difference between the predicted and observed values of y. You Answered True

False

Candidate A is facing two opposing candidates in a mayoral election. In a recent poll of 300 residents, 144 supported A. Construct a 99% confidence interval on the population proportion for the support of candidate A in the following election.

[0.4057, 0.5543]

Find the z value such that P(Z ≤ z) = 0.9066.

z = 1.32

A car dealer who sells only late-model luxury cars recently hired a new salesperson and believes that this salesperson is selling at lower markups. He knows that the long-run average markup in his lot is $5,600. He takes a random sample of 16 of the new salesperson's sales and finds an average markup of $5,000 and a standard deviation of $800. Assume the markups are normally distributed. What is the value of an appropriate test statistic for the car dealer to use to test his claim?

t15 = -3.00

A fast-food franchise is considering building a restaurant at a busy intersection. A financial advisor determines that the site is acceptable only if, on average, more than 300 automobiles pass the location per hour. The advisor tests the following hypotheses: Ho: μ ≤ 300. HA: μ > 300. The consequences of committing a Type I error would be that____________________________.

the franchiser builds on an unacceptable site

A fast-food franchise is considering building a restaurant at a busy intersection. A financial advisor determines that the site is acceptable only if, on average, more than 300 automobiles pass the location per hour. The advisor tests the following hypotheses: Ho: μ ≤ 300. HA: μ > 300. The consequences of committing a Type II error would be that____________________________.

the franchiser does not build on an acceptable site

Which of the following is considered an estimate?

x=20