MATH 625 Sampling Distributions and ConfidenceIntervals Exam Part One_Quiz (Score: 45 out of 50)

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3/3/2021

05.07 Sampling Distributions and Confidence Intervals Exam Part One: 20-21_V_Gurske_AP Statistics

05.07 Sampling Distributions and Confidence Intervals Exam Part One Due No due date Points 50 Allowed Attempts Unlimited

Questions 12

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Time

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Attempt 1

11 minutes

45 out of 50

 Correct answers are hidden.

Score for this attempt: 45 out of 50 Submitted Mar 3 at 3:31pm This attempt took 11 minutes.

Question 1

4 / 4 pts

(05.01 LC) A study of fishermen included 812 anglers who were chosen at random.

Of these anglers, 59% said they use live bait. Bait shop owners show that only 41% of anglers use live bait. Identify the statistic and the parameter.

Eight hundred twelve is the parameter and 59% is the statistic.

Eight hundred twelve is the statistic and 59% is the parameter.

Eight hundred twelve is the parameter and 41% is the statistic.

Fifty-nine percent is the statistic and 41% is the parameter. https://hallco.instructure.com/courses/64215/quizzes/381075

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05.07 Sampling Distributions and Confidence Intervals Exam Part One: 20-21_V_Gurske_AP Statistics

Fifty-nine percent is the parameter and 41% is the statistic.

Question 2

4 / 4 pts

(05.01 MC) Public opinion in the large city of Hillwood is that 62 percent of the residents are in favor of increasing taxes to fund afterschool programs and 38 percent are against the increase. What is the approximate probability that more than 180 of the residents surveyed will be against increasing taxes if a random sample of 450 residents are surveyed?

https://hallco.instructure.com/courses/64215/quizzes/381075

2/10

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05.07 Sampling Distributions and Confidence Intervals Exam Part One: 20-21_V_Gurske_AP Statistics

Question 3

4 / 4 pts

(05.01 LC) A polling company has decided to increase the size of its random sample of voters from about 2,000 people to about 4,500 people right before an election. A poll was designed to estimate the proportion of voters who favor a new law to set an 11 p.m. curfew for teenagers. What is the effect of this increase?

To reduce the bias of the estimate To increase the bias of the estimate To reduce the variability of the estimate To increase the variability of the estimate

This increase will have no effect because the population size is the same.

Question 4

4 / 4 pts

(05.01 MC) Suppose we select a simple random sample of size n = 125 from a large population with a proportion p of successes. Let p̂ be the proportion of successes in the sample. For which value of p is it appropriate to use the Normal approximation for the sampling distribution of p̂?

0.03 0.02 https://hallco.instructure.com/courses/64215/quizzes/381075

3/10

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05.07 Sampling Distributions and Confidence Intervals Exam Part One: 20-21_V_Gurske_AP Statistics

0.97 0.94 0.25

Question 5

4 / 4 pts

(05.02 LC) The Central Limit Theorem says that when sample size n is taken from any population with mean μ and standard deviation σ when n is large, which of the following statements are false?

I. The distribution of the sample mean is exactly Normal.

II. The distribution of the sample mean is approximately Normal.

III. The standard deviation is equal to that of the population.

IV. The distribution of the population is exactly Normal.

I and II I only II and III I, III, and IV II only

Question 6

4 / 4 pts

(05.02 MC) https://hallco.instructure.com/courses/64215/quizzes/381075

4/10

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05.07 Sampling Distributions and Confidence Intervals Exam Part One: 20-21_V_Gurske_AP Statistics

A metal washer fabrication machine makes metal washers with a target diameter of μ = 10.5 millimeters. The machine has some variability, so the standard deviation of the diameters is σ = 0.003 millimeter. The machine operator inspects a random sample of nine washers each hour for quality control purposes and records the sample mean diameter, x̄. Assuming the process is working properly, what are the mean and standard deviation of the sampling distribution of x̄?

μx̄ = 10.5, σx̄ = 0.001 μx̄ = 10.5, σx̄ = 0.003 μx̄ = 9, σx̄ = 0.003 μx̄ = 9, σx̄ = 0.001 μx̄ = 10.5, σx̄ = 3

Question 7

4 / 4 pts

(05.02 MC) The amount of fresh basil on the caprese salad at Olive Oil's follows a Normal distribution, with a mean of 1.15 ounces and a standard deviation of 0.21 ounce. A random sample of 14 plates of caprese salad is selected every day and the amount of basil is measured. What is the probability that the mean weight will exceed 1.23 ounces?

0.3516 0.6484 0.0561 0.9230 https://hallco.instructure.com/courses/64215/quizzes/381075

5/10

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05.07 Sampling Distributions and Confidence Intervals Exam Part One: 20-21_V_Gurske_AP Statistics

0.0770

Question 8

4 / 4 pts

(05.04 MC) A random sample of Oak County residents was selected and asked, "To attract new employment to our area, are you in favor of giving incentives to industries that build plants that are environmentally friendly?" A 90 percent confidence interval for the proportion of residents in favor of the incentives was found to be 0.62 ± 0.06. Which statement is true?

At the 90% confidence level, the estimate of 0.62 is within 0.06 of the true proportion of county residents in favor of offering incentives to environmentally friendly industries to build plants in the county.

At the 90% confidence level, the majority of area residents are in favor of offering incentives to environmentally friendly industries to build plants in the county.

In repeated sampling, 90% of sample proportions will fall in the interval (0.56, 0.68).

In repeated sampling, the true proportion of county residents in favor of offering incentives to environmentally friendly industries to build plants in the county will fall in the interval (0.56, 0.68).

https://hallco.instructure.com/courses/64215/quizzes/381075

6/10

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05.07 Sampling Distributions and Confidence Intervals Exam Part One: 20-21_V_Gurske_AP Statistics

In repeated sampling, 90% of the time, the true proportion of county residents in favor of offering incentives to environmentally friendly industries to build plants in the county will be equal to 0.62.

Incorrect

Question 9

0 / 5 pts

(05.04 MC) One hundred and fifty randomly selected residents in Whoaville were interviewed and asked, "Do you support the city's decision to build a swan sanctuary in your area?" A total of 76 said no, 9 said yes, and 65 had no opinion. A large sample z-confidence interval, p̂ ± z *

, was

constructed from these data to estimate the proportion that support building the swan sanctuary. Which statement is true for the confidence interval?

A sample size of more than 30 was used; therefore, the confidence interval is valid.

Each resident was asked the same question; therefore, the confidence interval is valid.

Because there are no conditions required for constructing a large sample confidence interval for a proportion, the confidence interval is valid

"No opinion" was included as a response category for the question; therefore, this confidence interval is not valid.

https://hallco.instructure.com/courses/64215/quizzes/381075

7/10

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05.07 Sampling Distributions and Confidence Intervals Exam Part One: 20-21_V_Gurske_AP Statistics

This confidence interval is not valid because the quantity np̂ is too small.

Question 10

4 / 4 pts

(05.05 LC) Using a random sample from a population, Isla cannot decide if she wants to construct a 95 percent confidence interval for the population mean or a 99 percent confidence interval for the population mean. What is the difference between the two confidence intervals?

The 95 percent confidence interval will be wider than the 99 percent confidence interval.

The 95 percent confidence interval will not be as wide as the 99 percent confidence interval.

The size of the sample determines which interval is wider.

An unbiased sample determines which interval is wider.

Which interval is wider will depend on whether a z-statistic or a t-statistic is used.

Question 11

https://hallco.instructure.com/courses/64215/quizzes/381075

5 / 5 pts

8/10

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05.07 Sampling Distributions and Confidence Intervals Exam Part One: 20-21_V_Gurske_AP Statistics

(05.05 MC) Potassium helps the human body prevent muscle cramping. Researchers sampled 52 random professional wrestlers. The average potassium level was 3.8 millimoles per liter and the standard deviation was 1.4 millimoles per liter. Construct and interpret a 95% confidence interval to estimate the mean potassium level in the population.

The 95% confidence interval is (3.7460, 3.8541). We are 95% confident that the true population mean potassium level for professional wrestlers will be between 3.7460 millimoles per liter and 3.8541 millimoles per liter.

The 95% confidence interval is (3.4102, 4.1898). Ninety-five percent of all samples of this size will yield a confidence interval of (3.4102, 4.1898).

The 95% confidence interval is (3.4102, 4.1898). There is a 95% chance that a randomly selected wrestler is one of the wrestlers whose potassium level lies between 3.4102 millimoles per liter and 4.1898 millimoles per liter.

The 95% confidence interval is (3.4102, 4.1898). We are 95% confident that the true population mean potassium level for professional wrestlers will be between 3.4102 millimoles per liter and 4.1898 millimoles per liter.

The 95% confidence interval is (3.7460, 3.8541). Ninety-five percent of all the samples of this size will yield a confidence interval of (3.7460, 3.8541).

Question 12 https://hallco.instructure.com/courses/64215/quizzes/381075

4 / 4 pts

9/10

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05.07 Sampling Distributions and Confidence Intervals Exam Part One: 20-21_V_Gurske_AP Statistics

(05.05 MC) Stan's heart rate, in beats per minute, was measured 20 times at random.

The results are 82, 84, 98, 112, 97, 93, 91, 87, 112, 87, 79, 80, 72, 82, 94, 89, 89, 74, 80, and 72 beats per minute. Construct a 99% confidence interval for Stan's mean heart rate.

(82.5659, 92.8341) (80.4942, 92.8341) (82.5659, 94.9052) (82.4288, 92.9712) (80.4942, 94.9052)

Quiz Score: 45 out of 50

https://hallco.instructure.com/courses/64215/quizzes/381075

10/10