BSTAT Test 2 review 2

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

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

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.

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)

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).

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

True

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

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.

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

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 probability P(Z > 1.28) is closest to ______.

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

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

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

0.4750

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

Which of the following are one-tailed tests?

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

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

False

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

False

For a given confidence level 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-σ)%

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 national average for an eighth-grade reading comprehension test is 73. A school district claims that its eighth-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

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 II error would be that____________________________.

the franchiser does not build on an acceptable site