Deck 13: More About Tests and Intervals

Question 1

A large software development firm recently relocated its facilities.Top management is interested in fostering good relations with their new local community and has encouraged their professional employees to engage in local service activities.They believe that the firm's professionals volunteer an average of more than 15 hours per month.If this is not the case, they will institute an incentive program to increase community involvement.A random sample of 24 professionals yields a mean of 16.6 hours and a standard deviation of 2.22 hours.The correct value of the test statistic for the appropriate hypothesis test is ________________________ .

A)t = 3.532
B)t = -3.532
C)t = 1.223
D)t = -1.223
E)t = 0.789

Answer 1

t = 3.532

Question 2

Grandma Gertrude's Chocolates, a family owned business, has an opportunity to supply its product for distribution through a large coffee house chain.However, the coffee house chain has certain specifications regarding cacao content as it wishes to advertise the health benefits (antioxidants) of the chocolate products it sells.In order to determine the mean % cacao in its dark chocolate products, quality inspectors sample 36 pieces.They find a sample mean of 55% with a standard deviation of 4%.The correct value of t^* to construct a 90% confidence interval for the true mean % cacao is ________________________ .

A)2.797
B)1.711
C)1.690
D)2.030
E)1.318

Answer 2

1.690

Question 3

Insurance companies track life expectancy information to assist in determining the cost of life insurance policies.ABI Insurance randomly sampled 100 recently paid policies and determined the average age of clients in this sample to be 77.7 years with a standard deviation of 3.6.The 90% confidence interval for the true mean age of its life insurance policy holders is ________________________ .

A)77.1 to 78.3 years
B)76.87 to 80.33 years
C)75.4 to 80 years
D)74.1 to 81.3 years
E)72.5 to 82.9 years

Answer 3

77.1 to 78.3 years

Question 4

A report on the U.S.economy indicates that 28% of Americans have experienced difficulty in making mortgage payments.A news organization randomly sampled 400 Americans from 10 cities named the "fastest dying cities in the U.S." (Forbes Magazine, August 2008) and found that 136 reported such difficulty.Does this indicate that the problem is more severe among these cities? The correct value of the test statistic for testing this claim is ________________________ .

A)z = -1.28.
B)z = -2.67
C)z = 2.67
D)z = 1.96
E)z = -1.28

Question 5

A manufacturer of cream filled donuts collected data from its automatic filling process, the amount of cream inserted into the donuts is normally distributed.To make sure that the automatic filling process is on target, quality control inspectors take a sample of 25 donuts.The correct value of t^* to construct a 99% confidence interval for the true mean amount of cream filling is ________________________ .

A)2.797
B)1.711
C)2.787
D)2.060
E)1.318

Question 6

In a metal fabrication process, metal rods are produced to a specified target length of 15 feet.Suppose that the lengths are normally distributed.A quality control specialist collects a random sample of 16 rods and finds the sample mean length to be 14.8 feet and a standard deviation of 0.65 feet.The 95% confidence interval for the true mean length of rods produced by this process is ________________________ .

A)14.544 to 15.056 ft
B)14.345 to 15.255 ft
C)13.912 to 15.688 ft
D)14.454 to 15.146 ft
E)13.834 to 15.766 ft

Question 7

Suppose that you are conducting a two tailed test about a proportion at the 0.01 level of significance.The correct critical value(s) to be used in drawing a conclusion is (are) ________________________ .

A)± 1.96
B)±2.575
C)-1.645
D)±1.645
E)1.96

Question 8

A report on the U.S.economy indicates that 28% of Americans have experienced difficulty in making mortgage payments.A news organization randomly sampled 400 Americans from 10 cities named the "fastest dying cities in the U.S." (Forbes Magazine, August 2008) and found that 136 reported such difficulty.Does this indicate that the problem is more severe among these cities? The correct null and alternative hypotheses for testing this claim are ________________________ .

A)H₀ : p = 0.28 and H_A : p > 0.28
B)H₀ : p = 0.28 and H_A : p < 0.28
C)H₀ : p = 0.28 and H_A : p ≠ 0.28
D)H₀ : p ≠ 0.28 and H_A : p = 0.28
E)H₀ : p > 0.28 and H_A : p = 0.28

Question 9

A report on the U.S.economy indicates that 28% of Americans have experienced difficulty in making mortgage payments.A news organization randomly sampled 400 Americans from 10 cities named the "fastest dying cities in the U.S." (Forbes Magazine, August 2008) and found that 136 reported such difficulty.Does this indicate that the problem is more severe among these cities? The P-value associated with the test statistic for testing this claim is 0.0029.At α = .05, ________________________ .

A)we can conclude that the percentage of Americans in these cities experiencing difficulty making mortgage payments is significantly higher than 28%
B)we can conclude that the percentage of Americans in these cities experiencing difficulty making mortgage payments is significantly lower than 28%
C)we can conclude that the percentage of Americans in these cities experiencing difficulty making mortgage payments is not significantly different from 28%
D)we can conclude that the percentage of Americans in these cities experiencing difficulty making mortgage payments is equal to 28%
E)None of the above.

Question 10

Which of the following is not an assumption and/or condition required for constructing a confidence interval for the mean?

A)Randomization condition
B)Nearly Normal condition
C)Success/Failure condition
D)10% condition
E)Independence assumption

Question 11

Insurance companies track life expectancy information to assist in determining the cost of life insurance policies.Last year the average life expectancy of all policyholders was 77 years.ABI Insurance wants to determine if their clients now have a longer life expectancy, on average, so they randomly sample some of their recently paid policies.The insurance company will only change their premium structure if there is evidence that people who buy their policies are living longer than before.Which of the following statement is true about this hypothesis test?

A)It is a two tailed test about a proportion.
B)It is a one tailed test about a mean.
C)It is a one tailed test about a proportion.
D)It is a two tailed test about a mean.
E)None of the above.

Question 12

Top management of a large multinational corporation wants to create a culture of innovativeness and change.A consultant hired to assess the company's organizational culture finds that only 15% of employees are open to new ideas and approaches toward their work.Consequently the company conducts a program for employees in order to reinforce the new corporate philosophy.After the program is completed, employees are surveyed to see if a greater percentage is now open to innovativeness and change.Suppose that based on the sample results the company rejects the null hypothesis when in fact it is true.Which of the following statements is correct?

A)This is known as a Type II error.
B)This is known as a fatal error.
C)This led to the conclusion that the percentage of employees open to new ideas did not increase when in fact it did.
D)This led to the conclusion that the percentage of employees open to new ideas did increase when in fact it did not.
E)This led to a P-value that was greater than the level of significance.

Question 13

Top management of a large multinational corporation wants to create a culture of innovativeness and change.A consultant hired to assess the company's organizational culture finds that only 15% of employees are open to new ideas and approaches toward their work.Consequently the company conducts a program for employees in order to reinforce the new corporate philosophy.After the program is completed, employees are surveyed to see if a greater percentage is now open to innovativeness and change.The correct alternative hypothesis is ________________________ .

A)p = 0.15
B)p > 0.15
C)p < 0.15
D)µ > 0.15
E)µ ≠ 0.15

Question 14

A small business ships specialty homemade candies to anywhere in the world.Past records indicate that the weight of orders is normally distributed.Suppose a random sample of 16 orders is selected and each is weighed.The sample mean was found to be 110 grams with a standard deviation of 14 grams.The 90% confidence interval for the true mean weight of orders is ________________________ .

A)103.87 to 116.14 grams
B)86.046 to 133.954 grams
C)99.5 to 120.5 grams
D)102.55 to 117.45 grams
E)103.14 to 116.86 grams

Question 15

A manufacturer of cream filled donuts collected data from its automatic filling process, the amount of cream inserted into the donuts is normally distributed.To make sure that the automatic filling process is on target, quality control inspectors take a sample of 25 donuts and measure the weight of cream filling.They find the 99% confidence interval of 14.16 to 15.84 grams.Which of the following is the correct interpretation?

A)We are 99% confident that the mean weight of cream filling in all donuts made by this process is between 14.16 and 15.84 grams.
B)99% of all donuts made by this process will have cream filling weights between 14.16 and 15.84 grams.
C)The weight of cream filling in the donuts is between 14.16 and 15.84 grams 99% of the time.
D)All of the above.
E)None of the above.

Question 16

A manufacturer of cream filled donuts collected data from its automatic filling process, the amount of cream inserted into the donuts is normally distributed.To make sure that the automatic filling process is on target, quality control inspectors take a sample of 25 donuts and measure the weight of cream filling.They find a sample mean weight of 15 grams with a standard deviation of 1.5 grams.What is the margin of error at 90% confidence?

A)0.3 grams
B)0.5133 grams
C)0.8391 grams
D)1.5 grams
E)0.06 grams