BSTAT 2305 Quiz 2

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 ______. 0.10 0.90 0.20 −0.10

0.90

Find the probability P(−1.70 ≤ Z ≤ 1.70). 1.9500 0.9750 0.9108 0.9426

0.9108

Find the probability P(−1.90 ≤ Z ≤ 1.90). 0.0500 0.9426 0.9750 1.9500

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 four electricians, what is the standard deviation for the sampling distribution of the sample mean?

6,000

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 ______.

65/200= .33

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

False. 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.

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 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.

For a given sample size n and population standard deviation σ, the width of the confidence interval for the population mean is wider, the smaller the confidence level

False For a given sample size n and population standard deviation σ, the width of the interval is wider, the greater the confidence level

The sample correlation coefficient cannot equal zero.

False. 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.

The correlation coefficient can only range between 0 and 1.

False. 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.

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)

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? 0.76 0.24 1.00 0.40

P(A∩B)=P(A)×P(B∣A) P(A∩B)=0.40×0.60= 0.24​

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 the same as P(X < 16). No comparison can be made with the given information. P(X > 16) is smaller than P(X < 16). P(X > 16) is greater than P(X < 16).

P(X > 16) is greater 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). P(X > 16) is smaller than P(X < 16). No comparison can be made with the given information. P(X > 20) is greater than P(X < 20)

P(X > 20) is the same as P(X < 20).

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 P({win}) = 1.0, P({loss}) = 0.1 P({win}) = 0.7, P({loss}) = −0.3 P({win}) = 0.4 P({loss}) = 0.6

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

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, 153 supported her. Construct a 90% confidence interval on the population proportion for the support of candidate A in the following election.

[0.4625, 0.5575]

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

Statistics are used to estimate population parameters, particularly when it is impossible or too expensive to poll an entire population. A particular value of a statistic is referred to as a(n) ______.

estimate

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

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

A ________ is a numerical quantity not computed from the data of a sample and is the size of the critical region used in reaching a decision on whether or not to reject the null hypothesis.

significance level

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

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

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

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

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

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

False. 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.

Find the z value such that P(Z ≤ z) = 0.9066. z = 0.1814 z = 1.32 z = 0.8186 z = 1.33

z = 1.32 consult z table

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

A random sample of size 36 is taken from a population with mean µ = 17 and standard deviation σ = 6. The probability that the sample mean is greater than 18 is ______.

0.1587

The probability P(Z >0.84) is closest to ______. 0.20 0.90 0.10 −0.10

0.20

A confidence interval was used to estimate the proportion of statistics students that are female. A random sample of 72 statistics students generated the following 90% confidence interval: (0.438, 0.642). Using the information above, what total size sample would be necessary if we wanted to estimate the true proportion to within ±0.08 using 95% confidence?

150

What is for a 95% confidence interval of the population mean based on a sample of 25 observations?

2.064

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

2.145 consult t table?

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 Ac = {TTT, HHH, HTH}; P(Ac) = 0.375 Ac = {TTT, THH, HHH, HHT}; P(Ac) = 0.500 Ac = {TTT, HHH, HHT, HTH, HTT}; P(Ac) = 0.625

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.

For a given confidence level sample n, the width of the confidence interval for the population mean is narrower, the greater the population standard deviation σ.

False

In an examination of purchasing patterns of shoppers, a sample of 16 shoppers revealed that they spent, on average, $54 per hour of shopping. Based on previous years, the population standard deviation is thought to be $21 per hour of shopping. Assuming that the amount spent per hour of shopping is normally distributed, find a 90% confidence interval for the mean amount.

[$45.36, $62.64]

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]

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

Which of the following is considered an estimate?

x=20

Find the z value such that P(Z ≤ z) = 0.9049. z = 1.33 z = 0.8186 z = 0.1814 z = 1.31

z = 1.31 consult z table