bstat exam 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

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

False 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 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 of size 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

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 ______.

0.8413

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.

Which of the following is true about statistics such as the sample mean or sample proportion? (exam 2)

A statistic is a random variable.

Which of the following is true about statistics such as the sample mean or sample proportion? (exam1)

A statistic is not a parameter.

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.

[11.7019, 13.2981] A recent Health of Boston report suggests that a greater percentage of female residents suffer from asthma as opposed to males. Suppose that out of 250 females and 200 males that responded to a recent study, 14% and 6% had asthma respectively. Which of the following is the correct conclusion for the test at a = 0.05 if the test statistic is found to be 2.76?females14% o

Reject H0: p1 − p2 ≤ 0 and therefore conclude that females suffer more from asthma than males.

Do men really spend more money on St. Patrick's Day as compared to women? A recent survey found that men spend an average of $43.87 while women spend an average of $29.54. Assume that these data were based on a sample of 100 men and 100 women and the population standard deviations of spending for men and women are $32 and $25, respectively. Using 1% confidence level, which of the following is the correct conclusion for this test?

Reject H0: µ1 − µ2 ≤ 0 and therefore conclude that on average men spend more money than women on St. Patrick's Day.

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).

A recent Health of Boston report suggests that a greater percentage of female residents suffer from asthma as opposed to males. Suppose that out of 250 females and 200 males that responded to a recent study, 14% and 6% had asthma respectively. Which of the following is the correct conclusion for the test at a = 0.05 if the test statistic is found to be 2.76?

Reject H0: p1 − p2 ≤ 0 and therefore conclude that females suffer more from asthma than males.

For any sample size n, the sampling distribution of is normal if the population from which the sample is drawn is normally distributed.

True

In a one-tailed test, the rejection region is located under one tail (left or right) of the corresponding probability distribution, while in a two-tailed test this region is located under both tails.

True

Non -response bias occurs when those responding to a survey or poll are systematically different from the non-respondents.

True

Selection bias occurs when the sample is mistakenly not selected from the target population.

True

The margin of error in the confidence interval for the difference u1 - u2 equals the standard error se(x1-x2) multiplied by either za/2 or ta/2,df depending on whether or not the population variances are known.

True

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

True

The statistical inference concerning the difference between two population proportions is used for qualitative data.

True

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

Unknown

When calculating the standard error of x1 - x2 , under what assumption do you pool the sample variances st and st?

Unknown population variances that are assumed equal.

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 underlying populations cannot be assumed to be normal, then by the central limit theorem, the sampling distribution of x1 - x2 is approximately normal only if both sample sizes are sufficiently large—that is, when _________ .

n1 ≥ 30 and n2 ≥ 30

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?

s(X) = a/sqrt(n)

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

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

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

z = 1.33

Do men really spend more money on St. Patrick's Day as compared to women? A recent survey found that men spend an average of $43.87 while women spend an average of $29.54. Assume that these data were based on a sample of 100 men and 100 women and the population standard deviations of spending for men and women are $32 and $25, respectively. Which of the following is the correct value of test statistic?

z = 3.53

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 difference between the two sample means x1 - x2 is an interval estimator of the difference between two population means u1 -u2.

False

The sample correlation coefficient cannot equal zero.

False

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

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 0.3644

.3192

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

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 tal,df for a 95% confidence interval of the population mean based on a sample of 25 observations?

2.064

The GPA of accounting students in a university is known to be normally distributed. A random sample of 20 accounting students results in a mean of 2.92 and a standard deviation of 0.16. Construct the 95% confidence interval for the mean GPA of all accounting students at this university.

2.92 (+-) 2.093(0.16/sqrt(20)

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

Nonresponse bias occurs when those responding to a survey or poll are systematically the same as the non-respondents.

False

Which of the following are one-tailed tests?

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

Selection bias occurs when the sample is mistakenly divided into strata, and random samples are drawn from each stratum.

False

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

False

The correlation coefficient can only range between 0 and 1.

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

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

False

A simple random sample is a sample of n observations that has a different probability of being selected from the population as any other sample of n observations.

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 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-a)%

False

For any sample size n, the sampling distribution of is normal even if the population from which the sample is drawn has any distribution.

False

If the underlying populations cannot be assumed to be normal, then by the central limit theorem, the sampling distribution of x1- x2 is approximately normal only if the sum of the sample observations is sufficiently large—that is, when n1 + n2 >= 30

False

In cluster random sampling, the population is first divided up into mutually exclusive and collectively exhaustive groups, called clusters. A cluster sample includes randomly selected observations from each cluster, which are proportional to the cluster's size.

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

A simple random sample is a sample of n observations that has the same probability of being selected from the population as any other sample of n observations.

True

Which of the following is considered an estimator?

X

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, 98 supported candidate B and 58 supported candidate C. 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

According to the central limit theorem, the distribution of the sample mean is always normal if ______. (dupe question careful)

the sample size n ≥ 30

According to the central limit theorem, the distribution of the sample means is normal if ______. (dupe question careful)

the underlying population is normal