statistics

We use the t distribution to make a confidence interval for the population mean if the population from which the sample is drawn is (approximately) normally distributed, the population standard deviation is unknown, and the sample size is at least: 1) 30 2) 100 3) 50 4) 2

1) 30

A 99% confidence interval estimate can be interpreted to mean that I. if all possible samples of size n are taken and confidence interval estimates are developed, 99% of them would include the true population mean somewhere within their interval. II. we have 99% confidence that we have selected a sample whose interval does include the population mean. 1) I and II 2) None of these 3) I only 4) II only

1) I and II

The power of a hypothesis test is .96. Which of the following statements is true about this test? 1) The probability of a Type II error is .04. 2) The probability of a Type I error is .04. 3) The probability of a Type II error is .96. 4) The probability of a Type I error is .96.

1) The probability of a Type II error is .04.

A 95% confidence interval for the average salary of all CEOs in the electronics industry was constructed using the results of a random survey of 45 CEOs. The interval was ($139,528, $154,454). Give a practical interpretation of the interval. 1) We are 95% confident that the mean salary of all CEOs in the electronics industry falls in the interval $139,528 to $154,454. 2) We are 95% confident that the mean salary of the sampled CEOs falls in the interval $139,528 to $154,454. 3) 95% of all CEOs in the electronics industry have salaries that fall between $139,528 to $154,454. 4) 95% of the sampled CEOs have salaries that fell in the interval $139,528 to $154,454.

1) We are 95% confident that the mean salary of all CEOs in the electronics industry falls in the interval $139,528 to $154,454.

Suppose a 95% confidence interval for u turns out the be (1,000, 2,100). Give a definition of what it means to be "95% confident" as an inference. 1) in repeated sampling, 95% of the intervals constructed would contain the population mean. 2) 95% of the observations in the entire population fall in the given interval 3) 95% of the observations in the sample fall in the given interval 4) in repeated sampling, the population parameter would fall in the given interval 95% of the time

1) in repeated sampling, 95% of the intervals constructed would contain the population mean.

If, as a result of a hypothesis test, you reject the null hypothesis when it is false, then you have committed 1) no error 2) an acceptance error 3) a Type I error 4) a Type II error

1) no error

A large university is interested in learning about the average time it takes students to drive to campus. The university sampled 238 students and asked each to provide the amount of time they spent traveling to campus. This variable, travel time, was then used conduct a test of hypothesis. The goal was to determine if the average travel time of all the university's students differed from 20 minutes. Suppose the large-sample test statistic was calculated to be z = 2.14. Find the p-value for this test of hypothesis. 1) p = 0.0324 2) p = 0.0162 3) p = 0.4838 4) p = 0.9838

1) p = 0.0324

To help consumers assess the risks they are taking, the Food and Drug Administration (FDA) publishes the amount of nicotine found in all commercial brands of cigarettes. A new cigarette has recently been marketed. The FDA tests on this cigarette yielded mean nicotine content of 24.3 milligrams and standard deviation of 2.1 milligrams for a sample of n = 9 cigarettes. Construct a 99% confidence interval for the mean nicotine content of this brand of cigarette. 1) 24.3 ± 2.413 2) 24.3 ± 2.349 3) 24.3 ± 2.491 4) 24.3 ± 2.275

2) 24.3 ± 2.349

An entrepreneur is considering the purchase of a coin-operated laundry. The current owner claims that over the past 5 years, the mean daily revenue was $675 with a population standard deviation of $75. A sample of 30 days reveals a daily mean revenue of $625. If you were to test the null hypothesis that the daily mean revenue was $675, which test would you use? 1) Z test of a population proportion 2) Z test of a population mean 3) t test of a population proportion 4) t test of population mean

2) Z test of a population mean

In a hypothesis test, a Type II error occurs when: 1) a false null hypothesis is rejected 2) a false null hypothesis is not rejected 3) a true null hypothesis is not rejected 4) a true null hypothesis is rejected

2) a false null hypothesis is not rejected

If an economist wishes to determine whether there is evidence that mean family income in a community equals $50,000 1) a two-tail test should be utilized. 2) a one-tail test should be utilized. 3) either a one-tail or two-tail test could be used with equivalent results. 4) None of the above.

2) a one-tail test should be utilized.

In a left-tailed hypothesis test, the sign in the alternative hypothesis is: 1) not equal to ≠ 2) less than (< ) 3) greater than( > ) 4) less than or equal to ≤

2) less than (< )

The alternative hypothesis is a claim about a: 1) parameter, where the claim is assumed to be true until it is declared false 2) parameter, where the claim is assumed to be true if the null hypothesis is declared false 3) statistic, where the claim is assumed to be true if the null hypothesis is declared false 4) statistic, where the claim is assumed to be false until it is declared true

2) parameter, where the claim is assumed to be true if the null hypothesis is declared false

The null hypothesis is a claim about a: 1) parameter, where the claim is assumed to be false until it is declared true 2) parameter, where the claim is assumed to be true until it is declared false 3) statistic, where the claim is assumed to be false until it is declared true 4) statistic, where the claim is assumed to be true until it is declared false

2) parameter, where the claim is assumed to be true until it is declared false

A retired statistician was interested in determining the average cost of a $200,000.00 term life insurance policy for a 60-year-old male non-smoker. He randomly sampled 65 subjects (60-year-old male non-smokers) and constructed the following 95 percent confidence interval for the mean cost of the term life insurance: ($850.00, $1050.00). State the appropriate interpretation for this confidence interval. Note that all answers being with "We are 95 percent confident that..." 1) The term life insurance cost for all 60-year-old male non-smoker's insurance policies falls between $850.00 and $1050.00 2)The average term life insurance costs for all 60-year-old male non-smokers falls between $850.00 and $1050.00 3) The term life insurance cost of the retired statistician's policy falls between $850.00 and $1050.00 4) The average term life insurance cost for sampled 65 subjects falls between $850.00 and $1050.00

2)The average term life insurance costs for all 60-year-old male non-smokers falls between $850.00 and $1050.00

Which of the following statements describes a Type II error in hypothesis testing? 1) A court declares a defendant guilty, when he is actually innocent. 2) A scientist, trying to support a theory about the number of different species of animals in a particular country, declares the null hypothesis to be "there are 715 different species" when there are actually more than 800. 3) A statistician determines, through hypothesis testing, that the mean number of televisions per household in a certain community is 1.4, when it is actually greater than 1.4. 4) Through hypothesis testing, we find the alternative hypothesis to be true when it is actually false.

3) A statistician determines, through hypothesis testing, that the mean number of televisions per household in a certain community is 1.4, when it is actually greater than 1.4.

The single value of a sample statistic that we assign to the population parameter is a: 1) single estimate 2) unique estimate 3) point estimate 4) singular estimate

3) point estimate

In a hypothesis test, the probability of committing a type I error is called the: 1) confidence level 2) confidence interval 3) significance level 4) beta error

3) significance level

For a one-tailed test, the p-value is: 1) the area under the curve between the mean and the observed value of the sample statistic 2) twice the area under the curve between the mean and the observed value of the sample statistic 3) the area under the curve to the same side of the value of the sample statistic as is specific in the alternative hypothesis 4)twice the area under the curve to the same side of the value of the sample statistic as is specific in the alternative hypothesis

3) the area under the curve to the same side of the value of the sample statistic as is specific in the alternative hypothesis

We use the t distribution to perform a hypothesis test about the population mean when: 1) the population from which the sample is drawn is approximately normal and the population standard deviation is known 2) the population from which the sample is drawn is not approximately normal and the population standard deviation is known 3) the population from which the sample is drawn is approximately normal and the population standard deviation is unknown 4) the population from which the sample is drawn is not approximately normal and the population standard deviation is unknown

3) the population from which the sample is drawn is approximately normal and the population standard deviation is unknown

A random sample of 250 students at a university finds that these students take a mean of 14.7 credit hours per quarter with a standard deviation of 1.9 credit hours. Estimate the mean credit hours taken by a student each quarter using a 95% confidence interval. Round to the nearest thousandth. 1) 14.7 ± .011 2) 14.7 ± .015 3) 14.7 ± .171 4) 14.7 ± .236

4) 14.7 ± .236

Which of the following is not part of the procedure for estimating the value of a population parameter? 1) Selecting a sample 2) Collecting the required information from the members of the sample 3) Calculating the value of the sample statistic 4) Calculating the exact value of the corresponding population parameter

4) Calculating the exact value of the corresponding population parameter

Researchers have claimed that the average number of headaches per student during a semester of Statistics is 16. Statistics students believe the average is higher. In a sample of n = 19 students the mean is 20 headaches with a deviation of 1.9. Which of the following represent the null and alternative hypotheses necessary to test the students' belief? 1) H0: μ < 16 vs. Ha: μ = 16 2) H0: μ = 16 vs. Ha: μ < 16 3) H0: μ = 16 vs. Ha: μ ≠ 16 4) H0: μ = 16 vs. Ha: μ > 16

4) H0: μ = 16 vs. Ha: μ > 16

Which of the following would be an appropriate null hypothesis? I. The mean of a population is equal to 55. II. The mean of a sample is equal to 55. III. The mean of a population is greater than 55. 1) II only 2) III only 3) Only I and III are appropriate. 4) I only

4) I only

Explain what the phrase 95% confident means when we interpret a 95% confidence interval for μ. 1) 95% of the observations in the population fall within the bounds of the calculated interval. 2) 95% of similarly constructed intervals would contain the value of the sampled mean. 3) The probability that the sample mean falls in the calculated interval is 0.95 4) In repeated sampling, 95% of similarly constructed intervals contain the value of the population mean.

4) In repeated sampling, 95% of similarly constructed intervals contain the value of the population mean.

Which of the following would be an appropriate alternative hypothesis? 1) The mean of a sample is equal to 55. 2) The mean of a sample is greater than 55. 3) The mean of a population is equal to 55. 4) The mean of a population is greater than 55.

4) The mean of a population is greater than 55.

An educator wanted to look at the study habits of university students. As part of the research, data was collected for three variables - the amount of time (in hours per week) spent studying, the amount of time (in hours per week) spent playing video games and the GPA - for a sample of 20 male university students. As part of the research, a 95% confidence interval for the average GPA of all male university students was calculated to be: (2.95, 3.10). What assumption is necessary for the confidence interval analysis to work properly? 1) The Central Limit theorem guarantees that no assumptions about the population are necessary. 2) The sampling distribution of the sample mean needs to be approximately normally distributed. 3) The population that we are sampling from needs to be a t-distribution with n-1 degrees of freedom. 4) The population that we are sampling from needs to be approximately normally distributed.

4) The population that we are sampling from needs to be approximately normally distributed.

An entrepreneur is considering the purchase of a coin-operated laundry. The current owner claims that over the past 5 years, the mean daily revenue was $675 with a population standard deviation of $75. A sample of 30 days reveals a daily mean revenue of $625. If you were to test the null hypothesis that the daily mean revenue was $675 and decide not to reject the null hypothesis, what can you conclude? 1) There is not enough evidence to conclude that the daily mean revenue was $675. 2) There is enough evidence to conclude that the daily mean revenue was not $675. 3) There is enough evidence to conclude that the daily mean revenue was $675. 4) There is not enough evidence to conclude that the daily mean revenue was not $675.

4) There is not enough evidence to conclude that the daily mean revenue was not $675.

A one-tailed hypothesis test contains: 1) one rejection region and two nonrejection regions 2) two rejection regions and one nonrejection region 3) two rejection regions and two nonrejection regions 4) one rejection region and one nonrejection region

4) one rejection region and one nonrejection region

If an economist wishes to determine whether there is evidence that mean family income in a community exceeds $50,000 1) a one-tail test should be utilized. 2) either a one-tail or two-tail test could be used with equivalent results. 3) a two-tail test should be utilized. 4) None of the above.

1) a one-tail test should be utilized.

In a right-tailed hypothesis test, the sign in the alternative hypothesis is: 1) not equal to ≠ 2) less than ( < ) 3) greater than( > ) 4) less than or equal to ≤

3) greater than( > )

In a hypothesis test, a Type I error occurs when: 1) a false null hypothesis is rejected 2) a false null hypothesis is not rejected 3) a true null hypothesis is not rejected 4) a true null hypothesis is rejected

4) a true null hypothesis is rejected

The t distribution 1) approaches the normal distribution as the sample size increases 2) assumes the population is normally distributed 3) has more area in the tails than does the normal distribution 4) all of the above

4) all of the above