Posted: December 21st, 2022

1.Assuming that the class survey represents the undergraduate population here at Penn State, calculate the 90% confidence interval for the true proportion of PSU undergraduate students who have tried marijuana (column C22). NOTE: be sure to check the box in the options for Use Interval Based on Normal Distribution.

A) 0.454869, 0.588791

B) 0.467470, 0.576777

C) 0.465284, 0.578527

D) 0.457000, 0.587247

2.A 2003 National Survey on Drug Use & Health conducted by the U.S. Department of Health and Human Services reported that 53.9% of adults between the ages of 18 – 25 have tried marijuana. Using the Class Survey data as a random sample of all PSU undergraduate students would you conclude that PSU students are in line with this report based on a 90% confidence interval for the class survey data (column C22)? NOTE: be sure to check the box in the options for Use Interval Based on Normal Distribution.

A) No, because the 90% confidence interval does not contain 53.9%

B) No, because the 90% confidence interval contains 53.9%

C) Yes, because the 90% confidence interval does not contain 53.9%

D) Yes, because the 90% confidence interval contains 53.9%

3.Find a 90% confidence interval for mean GPA in column C3. Assuming our survey is a random sample of all PSU undergraduates we can say that we are 90% confident:

A) that the true mean GPA of all PSU undergraduate students is between 3.17499 and 3.28714

B) that the true mean GPA of all PSU undergraduate students is between 3.16416 and 3.29796

C) that the true mean GPA of our sample is between 3.16416 and 3.29796

D) that the true mean GPA of our sample is between 3.17499 and 3.28714

4.Is the given percent a statistic or a parameter? Based on the 2000 Census, 39.5% of the California population of residents who are over 5 years old speak languages other than English at home.

A) Statistic

B) Parameter

5.Suppose that a polling organization surveys n = 400 people about whether they think the federal government should give financial aid to the airlines to help them avoid bankruptcy. In the poll, 300 people say that the government should provide aid to the airlines. Which choice gives the correct notation and value for the sample proportion, ρ-hat, in this survey?

A) ρ = 0.30

B) ρ-hat = 0.30

C) ρ-hat = 0.75

D) ρ =0.75

6.Which one of the following statements is false?

A) The standard error of a sample proportion decreases as the sample size increases.

B) The standard error measures the variability of a population parameter.

C) Assuming a fixed value of s = sample standard deviation, the standard error of the mean decreases as the sample size increases.

D) The standard error of a sample statistic measures, roughly, the average difference between the values of the statistic and the population parameter.

7.If the size of a sample randomly selected sample from a population is increased from n = 100 to n = 400, then the standard deviation of ρ-hat will

A) remain the same.

B) increase by a factor of 4.

C) decrease by a factor of 2.

D) decrease by a factor of 4.

8.Based on the 2000 Census, 31.8% of grandparents in California are the primary caregivers for their grandchildren. Suppose n = 1000 persons are to be sampled from this population and the sample proportion of grandparents as primary caregivers (ρ-hat) is to be calculated. What is the mean of the sampling distribution of ρ-hat?

A) 0.0002

B) 0.3180

C) 0.2169

D) 0.0147

9.Suppose on a highway with a speed limit of 65 mph, the speed of cars are independent and normally distributed with an average speed = 65 mph and standard deviation = 5 mph. What is the standard deviation for the sample mean speed in a random sample of n = 10 cars?

A) 32.5

B) 13

C) 1.58

10.For which of the following situations would the Rules for Sample Means not apply?

A) A random sample of size 20 is drawn from a bell-shaped population.

B) A random sample of size 50 is drawn from a skewed population.

C) A random sample of size 50 is drawn from a bell-shaped population.

D) A random sample of size 20 is drawn from a skewed population.

11.The z* multiplier for a 90% confidence interval is

A) 1.96

B) 1.65

C) 2.58

D) 2.33

12.Which statement is not true about confidence intervals?

A) A confidence interval is an interval of values computed from sample data that is likely to include the true population value.

B) An approximate formula for a 95% confidence interval is sample estimate ± margin of error.

C) A confidence interval between 20% and 40% means that the population proportion lies between 20% and 40%.

D) A 99% confidence interval procedure has a higher probability of producing intervals that will include the population parameter than a 95% confidence interval procedure.

13.A randomly selected sample of 400 students at a university with 15-week semesters was asked whether or not they think the semester should be shortened to 14 weeks (with longer classes). Forty-six percent of the 400 students surveyed answered yes. Which one of the following description of the number 46% is not correct?

A) sample estimate

B) point estimate

C) sample statistic

D) population parameter

14.Suppose that a 95% confidence interval for the proportion of first-year students at a school who played in intramural sports is 35% plus or minus 5%. The 95% confidence interval for the proportion of students playing intramural sports is

A) 30% to 35%

B) 25% to 45%

C) 30% to 40%

D) 35% to 40%

15.In a survey of n = 950 randomly selected individuals, 17% answered yes to the question “Do you think the use of marijuana should be made legal or not?” A 99% confidence interval for the proportion of all Americans in favor of legalizing marijuana is

A) 0.146 to 0.194

B) 0.150 to 0.190

C) 0.139 to 0.201

D) 0.142 to 0.198

16.In a nationwide survey of n = 1,030 adults, 6% answered yes to the question “During the last year did anyone break into or somehow illegally get into your home or apartment?” A 99% confidence interval for the proportion of all Americans who had their homes broken into is

A) 0.043 to 0.077

B) 0.048 to 0.072

C) 0.041 to 0.079

D) 0.045 to 0.075

17.A 95% confidence interval for the proportion of women that has ever dozed off while driving is 0.07 to 0.14. For men, a 95% confidence interval for the proportion that has ever dozed off while driving is 0.19 to 0.25. Assume both intervals were computed using large random samples. What conclusion can be made about the population proportions that have dozed off while driving?

A) No conclusion is possible because we don’t know the margin of error.

B) It is not reasonable to conclude that there is a difference between men and women.

C) It is reasonable to conclude that there is a difference between men and women.

D) It is reasonable to conclude that there is a difference of 0.05 between men and women.

18.A random sample of 30 airline flights during a storm had an average delay of 40 minutes. The standard deviation was 5 minutes, and the standard error of the mean is 0.9129. Calculate a 98% confidence interval for the average delay for all flights during a storm.

A) (27.7, 52.3)

B) (37.8, 42.2)

C) (38.2, 41.8)

19.Calculate the standard error of the sample statistic: A randomly selected sample of 30 students spent an average amount of $40.00 on a date, with a standard deviation of $5.00. The standard error of the sample mean is

A) 0.167

B) 0.913

C) 5.000

D) 0.063

20.Suppose that 200 different polling organizations and academic researchers all do surveys in which the same question is asked. All 200 research groups construct a 90% confidence interval for the proportion who would say “yes” to this question. About how many of the 200 different 90% confidence intervals will capture the value of the population proportion?

A) 190

B) 95

C) 90

D) 180

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