BSTAT Studyguide

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

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

0.4750

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 probability P(Z < 1.28) is closest to _____

0.90

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

0.9108

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

0.9426

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 ta/2, df 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

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 the when selecting sample sizes?

A larger sample size reduces the margin of error.

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

Which of the following are one-tailed tests?

Both Ho:μ ≤ 10, HA:μ > 10 and Ho:μ ≥ 400, HA:μ < 400

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.

False

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

False

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 100(1-a)%

False

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

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

False

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

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

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

False

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

False

A confidence interval provides a value that, with a certain measure of confidence, is the population parameter of interest.

False, confidence interval provides a range of values that, with a certain level of confidence, contains the population parameter of interest.

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).

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)

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]

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]

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]

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

f 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

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

.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 3030+Yes7665No2435 The probability that a respondent is at least 30 years old is the closest to ______.

.33

A random sample of size 100 is taken from a population described by the proportion p= 0.06. What are the expected value and the standard error for the sampling distribution of the sample proportion?

0.060 and 0.024

Susan has been on a bowling team for 14 years. After examining all of her scores over that period of time, she finds that they follow a normal distribution. Her average score is 225, with a standard deviation of 13.If during a typical week Susan bowls 16 games, what is the probability that her average score is more than 230?

0.0620

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

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

0.10

A random sample of size 100 is taken from a population described by the proportion p = 0.60.The probability that the sample proportion is less than 0.55 is ______.

0.1537

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

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

Unknown

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

The national average for an eighth-grade reading comprehension test is 73. A school district claims that its eight-graders outperform the national average. In testing the school district's claim, how does one define the population parameter of interest?

The mean score on the eighth-grade reading comprehension test.

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

True

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

z=1.32

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

A 99% confidence interval estimate can be interpreted to mean that

if all possible samples of the same size are taken and confidence interval estimates are developed, 99% of them would include the true population mean somewhere within their interval.

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 II error would be that

the franchiser does not build on an acceptable site

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

z = 1.31

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

z = 1.33