BSTAT 2305-002

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

A random sample size of 100 is taken from a population described by the proportion p=0.60. What are the expected value and the standard error for the sampling distribution of the sample proportion?

0.600 and 0.049

Find the probability P(−1.70 ≤ Z ≤ 1.70).

0.9108

Find the probability P(−1.80 ≤ Z ≤ 1.80).

0.9282

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.

Like the z distribution, the tdf distribution is symmetric around 0, bell-shaped, and with tails that approach the horizontal axis and eventually cross it.

False, because Like the z distribution, the tdf distribution is symmetric around 0, bell-shaped, and with asymptotic tails—that is, the tails get closer and closer to the horizontal axis but never touch it.

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

False, because The covariance and correlation coefficient are measures that quantify the linear relationship between two variables.

The sample correlation coefficient cannot equal zero.

False, because The sample correlation coefficient falls between −1 and 1. If it equals 1 (or −1), then a perfect positive (negative) linear relationship exists. If the sample correlation coefficient is zero, then no linear relationship exists.

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

False, because a residual is the differenced between the observed and predicted values of y.

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

False, because a standard normal distribution is a special case of the normal distribution with a mean equal to zero and standard deviation equal to one.

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

False, because as the absolute value of the sample correlation coefficient increases, the linear relationship between x and y becomes stronger.

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

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 = 15 inches. How is the probability P(X > 16) related to P(X < 16)?

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

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

P(X > 20) is the same as P(X < 20) u=20 o=4 p(x>28) related to P(x<16) z=((28-20))/4 + 2.00 P(z>2.00)=area to the right of 2.00

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

P({win)} = 0.4 P({loss}) = 0.6

For a given confidence level 100 (1- α)% and population standard deviation σ, the width of the confidence interval for the population mean is wider, the smaller the sample size n.

True

The probability that a standard normal random variable, Z, is greater than 50 is approximately 0.

True

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

True

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

Unknown

Candidate A is facing two opposing candidates in a mayoral election. In a recent poll of 300 residents, she has garnered 51% support. Construct a 95% confidence interval on the population proportion for the support of candidate A in the following election.

[0.4534, 0.5666]

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]

We draw a random sample of size 36 from a population with standard deviation 3.5. If the sample mean is 27, what is a 95% confidence interval for the population mean?

[25.8567, 28.1433]

What is the minimum sample size required to estimate a population mean with 95% confidence when the desired margin of error or bound on error is B = 1.5? The population standard deviation is known to be 10.75.

n = 198

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

For a given sample size n and population standard deviation, the width of the confidence interval for the population mean is wider, the smaller the confidence level 100 (1- α)%

False, because for a given sample size n and population standard deviation, the width of the interval is wider, the greater the confidence level 100 (1- alpha)%

The central limit theorem approximation improves as the sample size decreases.

False, because the central limit theorem approximation improves as the sample size increases.

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

False, because the covariance ranges from−infinity to infinity and is sensitive to the units of measurement. As a result, it is hard to determine what are small and large values, and cannot be easily used to assess the strength of a linear relationship.

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

False, because the deterministic component of a linear regression model is when the value of the response variable is uniquely determined by the values of the explanatory variables. The stochastic component is due to the omission of relevant variables that influence the response.

The correlation coefficient can only range between 0 and 1.

False, because the sample correlation coefficient falls between −1 and 1. If it equals 1 (or −1), then a perfect positive (or negative) linear relationship exists. If the sample correlation coefficient is zero, then no linear relationship exists.

Find the z value such that P(Z ≤ z) = 0.9099.

z = 1.34

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

.3192

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

0.00

The probability P(Z >0.84) is closest to ______

0.20

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 B will rise in price?

0.24

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 tα/2,df) for a 99% confidence interval of the population mean based on a sample of 25 observations?

2.797

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 A and what is the probability of this event?

A= (TTT, HHT, HTH, THH, HHH); P(A)= 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.

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

What is the relationship between the expected value of the sample mean and the expected value of the population?

E(X) = E(X) = μ

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 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

Find the z value such that P(Z ≤ z) = 0.9049.

z = 1.31