QM 215

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.

Over the entire six years that students attend an Ohio elementary school, they are absent, on average, 28 days due to influenza. Assume that the standard deviation over this time period is σ = 9 days. Upon graduation from elementary school, a random sample of 36 students is taken and asked how many days of school they missed due to influenza. What is the standard deviation for the sampling distribution of the average number of school days missed due to influenza?

1.50

According to a report in USA Today, more and more parents are helping their young adult children get homes. Suppose eight persons in a random sample of 40 young adults who recently purchased a home in Kentucky received help from their parents. You have been asked to construct a 95% confidence interval for the population proportion of all young adults in Kentucky who received help from their parents. What is the margin of error for a 95% confidence interval for the population proportion?

1.96(0.0632)

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 university interested in tracking its honors program believes that the proportion of graduates with a GPA of 3.00 or below is less than 0.10. In a sample of 300 graduates, 27 students have a GPA of 3.00 or below. The value of the test statistic and its associated p-value are __________.

z = −0.58 and p-value = 0.2810

According to the central limit theorem, the sampling distribution of x−μσ/n√.�-��/�. approaches the normal distribution as the sample size ______.

increases

A company has developed a new diet that it claims will lower one's weight by more than 10 pounds. Health officials decide to conduct a test to validate this claim. The consumers should be __________.

more concerned about Type I error

The sampling distribution of the population proportion is based on a binomial distribution. What condition must be met to use the normal approximation for the confidence interval?

nP _> 5 AND n (1-P- )>_ 5

A sample of a given size is used to construct a 95% confidence interval for the population mean with a known population standard deviation. If a bigger sample had been used instead, then the 95% confidence interval would have been _______ and the probability of making an error would have been ________.

narrower; unchanged

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

FALSE

If the expected value of a sample mean equals the population mean, the sample mean is biased.

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

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 tdf distribution consists of a family of distributions where the actual shape of each one depends on the degrees of freedom, df. For lower values of df, the tdf distribution is similar to the z distribution.

False

What type of variable would necessitate using a hypothesis test of the population proportion rather than a test of the population mean?

Categorical

If we reject a null hypothesis at the 1% significance level, then we have __________ evidence that the null hypothesis is false.

Sufficient

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 confidence interval for this hypothesis test would be __________.

[$16,788.22, $19,611.78]

Given a sample mean of 27 and a sample standard deviation of 3.5 computed from a sample of size 36, find a 95% confidence interval on the population mean.

[25.8158, 28.1842]

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]

The parameter p represents the ________ of successes in the population.

proportion

A university interested in tracking its honors program believes that the proportion of graduates with a GPA of 3.00 or below is less than 0.20. In a sample of 200 graduates, 30 students have a GPA of 3.00 or below. At a 5% significance level, the decision is to __________.

reject H0; we can conclude that the proportion of graduates with a GPA of 3.00 or below is significantly less than 0.20

If the p-value for a hypothesis test is 0.027 and the chosen level of significance is α = 0.05, then the correct conclusion is to __________.

reject the null hypothesis

A newly hired basketball coach promised a high-paced attack that will put more points on the board than the team's previously tepid offense historically managed. After a few months, the team owner looks at the data to test the coach's claim. He takes a sample of 16 of the team's games under the new coach and finds that they scored an average of 90 points with a standard deviation of 9 points. Over the past 10 years, the team had averaged 88 points. What is the value of the appropriate test statistic to test the new coach's claim at the 1% significance level?

t 15 = 0.89

A schoolteacher is worried that the concentration of dangerous, cancer-causing radon gas in her classroom is greater than the safe level of 4pCi/L. The school samples the air for 36 days and finds an average concentration of 4.4pCi/L with a standard deviation of 1pCi/L. The value of the test statistic is __________.

t35 = 2.40

When conducting a hypothesis test concerning the population mean, and the population standard deviation is unknown, the value of the test statistic is calculated as __________.

tdf=x− − μos/n√