Deck 8: Drawing Inferences From Large Samples

Question 1

A parameter is a numerical feature of a probability distribution.

Answer 1

True

Question 2

When using $\bar{x}$ to estimate μ , find the standard error for n = 160, σ =51 . Round your answer to three decimal places.

Answer 2

4.032

Question 3

When using $\bar{x}$ to estimate μ find the 100 (1-α)% error margin for
n = 146 σ =63 98% error margin.
Round your answer to three decimal places.

Answer 3

12.148

Question 4

For the following data estimate.

A) The point estimate of μ.
B) The 100(1-α)% error margin.
n = 68 X̄=138 s=6 1-α= 0.86

Question 5

Consider the problem of estimating $\mu$ , the mean time per day spent in the gym for freshmen students. Obtain the point estimate of $\mu$ and the estimated standard error.

A)
B)
C)
D)

Question 6

Consider the following data set.
Find the standard error.

Question 7

The following summary of a data set refers to the girth of grizzly bears in centimenters.
Find the 94% error margin. Round your answer to two decimal places.

Question 8

Determine the sample size n that is required for estimating the population mean. The population standard deviation $\mu$ and the desired error margin are specified.
90% error margin 4

A) 3314
B) 3315
C) 58
D) 47

Question 9

When estimating the mean of a population, how large a sample is required in order that 96% error margin be $\frac{1}{20}$ of the population standard deviation?

Question 10

When estimating the mean of a population, how large a sample is required in order that the 94% error margin be 14% of the population standard deviation?

Question 11

Assuming the population is normal and $\mu$ is known, a 98% confidence interval for $\mu$ is given by

Question 12

Assume n = 38, $\bar{x}$ = 23.367, and s = 11.056. Obtain a 98% confidence interval for μ, the population mean.

Question 13

The research department of a biochemical industry took a sample of 60 bacteria cultures of the same kind and observed that the mean weight was 25.267 grams with standard deviation of 8.816 grams. Obtain a 99% confidence interval for the mean weight of the bacteria cultures.

Question 14

Each day, the featured fixed price menu is rated by 35 persons and a 99 \% confidence
Interval obtained for the population mean rating $\mu$. Over a period of one year, 300 confidence intervals are calculated. Of these 300 confidence intervals, approximately how many will cover their respective population means?

Question 15

An employee of the College Board analyzes the mathematics section of the SAT for 99 students and finds $\bar{x}$ = 31.3 and s = 12.8. She reports that a 99% confidence interval for the mean number of correct answers is (27.981, 34.619). Does the interval (27.981, 34.619) cover the true mean?
Which of the following alternatives is the best answer for the above question?

A) Yes, (27.981, 34.619) covers the true mean
B) No, (27.981, 34.619) does not cover the true mean
C) We will never know whether (27.981, 34.619) covers the true mean.

Question 16

In a study on the annual salary of recently graduated engineers, a random sample of 50 professional was taken. The sample mean and standard deviation were found to be $79,100 and $9200 respectively. Use these data to construct a 95% confidence interval for the mean annual salary of recently graduated engineers. Round your answer to the nearest integer.

Question 17

In a study about poverty level by county, the number of residents living below the poverty level was measured for a random sample of 40 counties with less than 500 residents living below the poverty level. The sample mean and standard deviation were found to be 307 and 145 residents, respectively. Use these data to construct a 98% confidence interval for the mean of the number of residents by county living below the poverty level. Round your answer to the nearest integer.

Question 18

Based on a survey of 120 persons employed by the state of Kansas, the mean and standard deviation of their ages are found to be 37 and 9 years, respectively. Determine a 90% confidence interval for the mean age of the state of Kansas employees. Round your answer to the nearest integer.

Question 19

A Type II error consist of the ______ of H₀ when H₁ is true.

Question 20

If the goal of the study is to establish that the mean amount of gasoline consumed by a S.U.V. in 100 miles of highway is over 8.5 gallons, the null and alternative hypotheses are:

Question 21

Consider the following statement,
The mean amount of money spent in leisure activities for a 4-number family in the east coast is less than $200 per month.
Suppose that the decision has been to reject the null hypothesis.

A)When is it a wrong decision?
B) What type of error is then made?
The mean amount of money spent in leisure activities for a 4-number family in the east coast is less than $200 per month.

Question 22

Consider the following statement,
The mean time of pregnancy is 287 days.
Suppose that the decision has been made to retain the null hypothesis

A) When is it a wrong decision?
B) What type of error is then made?

Question 23

Given the standard deviation σ, the statement of your claim about μ, the sample size, and the desired level of significance α.
Formulate:
a) the hypotheses,
b) the test statistic Z,
c) the rejection region.

Question 24

Given the standard deviation σ, the statement of your claim about μ , the sample size, and the desired level of significance α.

Formulate:
a) the hypotheses,
b) the test statistic Z,
c) the rejection region.

Question 25

Given the standard deviation σ, the statement of your claim about μ, the sample size, and the desired level of significance α.

Formulate:
a) the hypotheses,
b) the test statistic Z,
c) the rejection region.

Question 26

An industrial researcher wants to perform a test with the intent of establishing that this company's compact fluorescent lamp has a mean life greater than 6300 hours. The sample size is 106 and he knows that $\sigma$ =53 hours.
If he set the rejection region to be what is the level of significance of his test?

Question 27

An industrial researcher wants to perform a test with the intent of establishing that this company's compact fluorescent lamp has a mean life greater than 7100 hours. The sample size is 128 and he knows that $\sigma$ =79 hours.
Find the numerical value of c so that the test has a 5% level of significance.

A) 7106.98
B) 7107.13
C) 7111.49
D) 7088.51

Question 28

The baggage manager of an airport wants to improve the time that passengers wait in the baggage claim area. She has a sample of 129 domestic flights. The mean waiting time is $\bar{x}$ = 12 minutes and s = 3.6 minutes. Is the claim that μ>13.5 minutes substantiated by these data? Test with α = 0.01.

Question 29

Suppose $\bar{x}$ = 4.55 and s = 5.17 for N = 40. We claim that H₀ = 2.3 and H₁ ≠ 2.3
. Find the P- value. Round your answer to four decimal places.

Question 30

A survey is conducted of n = 957 adults (65 years or older) and x = 258 reported high blood pressure problems.

A) Provide a point estimate of p. Round your answer to three decimal places.
B) Determine the 96% error margin. Round your answer to four decimal places.

Question 31

Employees of a movie theater ask their customers whether they like the movie exhibited or not. Out of 492 customers surveyed, 341 liked the movie. Compute a 88% confidence interval for the population proportion of satisfied customers.

Question 32

A staff member of the office of institutional research in a large university wants to estimate the proportion of students that fail the Calculus I course. A faculty member mentioned to her that 35% of the students fail the course. How many academic reports should the staff member analyze to be 90% confident that the error estimation is within 0.03?

Question 33

A travel agency wants to estimate the proportion of cancellations per year they receive. How large a sample of records must be examined to be 86% sure that the estimate does not differ from the true proportion by more than 0.02? The travel agent knows that the proportion is about 29%

Question 34

Out of a sample of 596 gasoline purchases at a self-service gas station, 436 were made with a credit or debit card.
Estimate the proportion of sales made with a credit or debit card.

A) .732
B) .738
C) .744
D) .750

Question 35

Out of a sample of 500 students, 401 owned a smart phone that was less than 3 years old. Obtain the estimated standard error. Round your answer to three decimal places.

Question 36

Out of a sample of 645 students, 429 had binge watched a TV series last month.
Find a 95% confidence interval for the population proportion of purchases paid with credit or debit card.

Question 37

Given your claim about a population proportion, the sample size n, and the desired level of significance α.
Formulate:

A) the hypotheses,
B) the test statistic Z,
C) the rejection region.

Question 38

Given your claim about a population proportion, the sample size n, and the desired level of significance α.
Formulate:

A) the hypotheses,
B) the test statistic Z,
C) the rejection region

Question 39

Given your claim about a population proportion, the sample size n, and the desired level of significance α.
Formulate:

A) the hypotheses,
B) the test statistic Z,
C) the rejection region

Question 40

A random sample of 781 applicants for drivers license was taken, 270 of the applicants failed the driving test. Find a 90% confidence interval for the corresponding population proportion.

Question 41

The number of times an undergraduate binge watched a TV se- ries in the past month was recorded for a sample of size 49. The summary statistics are
n = 49 $\bar{x}$ = 2.1 s = 1.61
Let µ =population mean number of times.

(a) Conduct a test of hypotheses with the intent of showing that
µ > 1.5. Take α = .05.

(b) Calculate the P-value. Does this strengthen your conclusion to the test of hypotheses? Explain.

(c) Based on the conclusion to your test in Part a, what error could you have made.

Question 42

Thirty-six measurements are made on the amount of meat in a pizza product. The summary statistics are
n = 36 $\bar{x}$ = 17.4 grams s = 1.8 grams
Let µ =population mean amount of meat.
(a) Conduct a test of hypotheses with the intent of showing that
µ /= 17. Take α = .05.
(b) Explain your choice of sampling distribution.
(c) Sketch the null distribution of your statistic and the rejection region.
(d) Based on the conclusion to your test in Part a, what error could you have made?
 

Question 43

The number of times an undergraduate binge watched a TV se- ries in the past month was recorded for a sample of size 49. The summary statistics are
n = 49 $\bar{x}$ = 2.1 s = 1.61
Let µ =population mean number of times.
(a) Give a point estimate of µ and its estimated standard error.
(b) Obtain a 95 % confidence interval for the population mean µ.
(c) Does your interval cover µ? Explain

Question 44

Thirty-six measurements are made on the amount of meat in a pizza product. The summary statistics are
n = 36 $\bar{x}$ = 17.4 grams s = 1.8 grams

Let µ =population mean amount of meat.

(a) Obtain a 98 % confidence interval for µ.
(b) Does your 98 % confidence interval cover µ. Explain.
(c) When a large number of these 98 % intervals are calculated, from data collected on different occasions, explain the reason you are 98% confident that any one of them covers µ. confi- dence that

Question 45

5 An inspection of eight wind turbines revealed that 13 operate too loudly according to new sound restrictions. The summary statistics are
n = 80 x = 13

Let p =population proportion that are too loud.
(a) Conduct a test of hypotheses with the intent of showing that
p > .1. Take α = .05.

(b) Calculate the P-value. Does this strengthen your conclusion to the test of hypotheses? Explain.

(c) Based on the conclusion to your test in Part a, what error could you have made.

(d) Explain why, prior to sampling, that this possible error seldom occur.

Question 46

A cell phone provider surveyed four hundred customers about sat- isfaction with their student service plan. The number that replied unsatisfactory, X, was recorded. The summary statistics are n =
400 x = 24. Let p =population proportion.
(a) Conduct a test of hypotheses with intent of showing that p /=
17. Take $\alpha$ = .05.

(b) Explain your choice of sampling distribution.
(c) Sketch the null distribution of your statistic and the rejection region.
(d) Based on the conclusion to your test in Part a, what error could you have made?

Question 47

An inspection of eight wind turbines revealed that 13 operate too loudly according to new sound restrictions. The summary statistics are
n = 80 x = 13
Let p = population proportion that are too loud.
(a) Give a point estimate of p and its estimated standard error
(b) Obtain a 95 % confidence interval for the population mean p.
(c) Does your interval cover p? Explain.

Question 48

A cell phone provider surveyed four hundred customers about sat- isfaction with their student service plan. The number that replied unsatisfactory, X, was recorded. The summary statistics are n = 400 x = 24. Let p =population proportion.
(a) Obtain a 99 % confidence interval for p.
(b) Does your 99 % confidence interval cover p. Explain.
(c) When a large number of these 99 % intervals are calculated from different samples, explain the reason you are 99% confi- dent that any particular one of them covers p.