Question 1

From past records it is known that the average life of a battery used in a digital clock is 305 days. The battery life is normally distributed. The battery was recently modified to last longer. A sample of 20 of the modified batteries was tested. It was discovered that the mean life was 311 days and the sample standard deviation was 12 days. We want to test at the 0.05 level of significance whether the modification increases the life of the battery. What is our decision rule?

Accepted Answer

A)  Do not reject the null hypothesis if computed t is 1.96 or greater 
B)  Reject the null hypothesis if computed t is less than 1.96 
C)  Do not reject the null hypothesis if computed t is 1.729 or greater 
D)  Reject the null hypothesis if computed t is 2.086 or greater 
E)  None of these statements are true

Question 2

A manufacturer claims that less than 1% of all his products do not meet the minimum government standards. A survey of 500 products revealed ten did not meet the standard.

Accepted Answer

A)  The null hypothesis is p ≥ 0.01. The alternate hypothesis is p  0.01 
C)  The null hypothesis is p ≥ 0.01. The alternate hypothesis is p > 0.01 
D)  The null hypothesis is p = 0.01. The alternate hypothesis is p ≠ 0.01 
E)  The null hypothesis is p< 0.01. The alternate hypothesis is p ≠ 0.01

Question 3

Test at the 0.01 level the statement that 55% of those families who plan to purchase a vacation residence in Florida want a condominium. The null hypothesis is p = 0.55 and the alternate is p ≠ 0.55. A random sample of 400 families who planned to buy a vacation residence revealed that 228 families want a condominium. What decision should be made regarding the null hypothesis?

Accepted Answer

A)  Do not reject it 
B)  Reject it 
C)  Cannot accept nor reject it based on the information given 
D)  None of these statements are true

Question 4

i. One assumption in testing a hypothesis about a proportion is that the data collected are the result of counting something.
Ii) One assumption in testing a hypothesis about a proportion is that an outcome of an experiment can be classified into two mutually exclusive categories, namely, a success or a failure.
Iii) A proportion is a fraction, ratio or probability that gives the part of the population or sample that has a particular trait of interest.

Accepted Answer

A)  (i), (ii) and (iii) are all correct statements 
B)  (i) is a correct statement but not (ii) or (iii). 
C)  (i) and, (iii) are correct statements but not (ii). 
D)  (ii) and, (iii) are correct statements but not (i). 
E)  All statements are false

Question 5

It is claimed that in a bushel of peaches less than ten percent are defective. A sample of 400 peaches is examined and 50 are found to be defective.
If α = 0.025, what will be the decision?

Accepted Answer

A)  Fail to reject the null and conclude the defects are not greater than 10% 
B)  Reject the null and conclude the defects are not greater than 10% 
C)  Reject the null and conclude the defects are greater than 10% 
D)  Fail to reject the null and conclude the defects are not less than 10% 
E)  None of these statements are true

Question 6

i. If the critical values of the test statistic z are ±1.96, they are the dividing points between the areas of rejection and non-rejection.
Ii) The probability of a Type I error is also referred to as alpha.
Iii) A Type I error is the probability of accepting a true null hypothesis.

Accepted Answer

A)  (i), (ii) and (iii) are all correct statements 
B)  (i) is a correct statement but not (ii) or (iii). 
C)  (i) and, (iii) are correct statements but not (ii). 
D)  (i) and, (ii) are correct statements but not (iii). 
E)  All statements are false

Question 7

Given: null hypothesis is that the population mean is 16.9 against the alternative hypothesis that the population mean is not equal to 6.9. A random sample of 25 items results in a sample mean of 17.8
And the sample standard deviation is 2.4. It can be assumed that the population is normally distributed. Determine the observed "t" value.

Accepted Answer

A)  t = 1.88 
B)  t = 1.83 
C)  t = 1.75 
D)  t = 2.21 
E)  None of these statements are true

Question 8

The dean of a business school claims that the average starting salary of its graduates is more than $50,000. It is known that the population standard deviation is $10,000. Sample data on the starting salaries of 20 randomly selected recent graduates yielded a mean of $55,000. What is the value of the sample test statistic?

Accepted Answer

A)  z = 2.24 
B)  t = 7.2 
C)  t = 5.04 
D)  t = 2.24 
E)  None of these statements are true

Question 9

i. The probability of a Type I error is also referred to as alpha. 
ii. A Type I error is the probability of accepting a true null hypothesis. 
iii. A Type I error is the probability of rejecting a true null hypothesis.

Accepted Answer

A)  (i), (ii) and (iii) are all correct statements 
B)  (i) is a correct statement but not (ii) or (iii). 
C)  (i) and, (iii) are correct statements but not (ii). 
D)  (i) and, (ii) are correct statements but not (iii). 
E)  All statements are false

Question 10

i. An alternate hypothesis is a statement about a population parameter that is accepted when the null hypothesis is rejected.
Ii) The level of significance is the risk we assume of rejecting the null hypothesis when it is actually true.
Iii) The researcher must decide on the level of significance before formulating a decision rule and collecting sample data.

Accepted Answer

A)  (i), (ii) and (iii) are all correct statements 
B)  (i) is a correct statement but not (ii) or (iii). 
C)  (i) and, (iii) are correct statements but not (ii). 
D)  (i) and, (ii) are correct statements but not (iii). 
E)  All statements are false

Question 11

i. A sample proportion is found by dividing the number of successes in the sample by the number sampled.
Ii) The standard normal distribution is the appropriate distribution when testing a hypothesis about a population proportion.
Iii) When testing population proportions, the z statistic can be used when np and n(1 - p) are greater than five.

Accepted Answer

A)  (i), (ii) and (iii) are all correct statements 
B)  (i) is a correct statement but not (ii) or (iii). 
C)  (i) and, (iii) are correct statements but not (ii). 
D)  (ii) and, (iii) are correct statements but not (i). 
E)  All statements are false

Question 12

Based on the Nielsen ratings, the local CBS affiliate claims its 11:00 PM newscast reaches 41% of the viewing audience in the area. In a survey of 100 viewers, 36% indicated that they watch the late evening news on this local CBS station. What is your decision if α = 0.01?

Accepted Answer

A)  Fail to reject the null hypothesis and conclude about 41%. 
B)  Reject the null hypothesis and conclude different from 41%. 
C)  Fail to reject the alternate and conclude different from 41%. 
D)  Reject the alternate and conclude it is 41%. 
E)  None of these statements are true

Question 13

Given: null hypothesis is that the population mean is 16.9 against the alternative hypothesis that the population mean is not equal to 6.9. A random sample of 25 items results in a sample mean of 18.0
And the sample standard deviation is 2.4. It can be assumed that the population is normally distributed. Determine the observed "t" value.

Accepted Answer

A)  t = 2.29 
B)  t = 1.83 
C)  t = 1.75 
D)  t = 2.01 
E)  None of these statements are true

Question 14

What is the level of significance?

Accepted Answer

A)  Probability of a Type II error 
B)  Probability of a Type I error 
C)  z-value of 1.96 
D)  Beta error 
E)  None of these statements are true

Question 15

The mean weight of newborn infants at a community hospital is 6.6 pounds. A sample of seven infants is randomly selected and their weights at birth are recorded as 9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6 pounds. Does this sample support the original claim? What is the alternate hypothesis?

Accepted Answer

A)  μ = 6.6 
B)  μ ≠ 6.6 
C)  μ ≥ 6.6 
D)  μ > 7.6 
E)  μ ≠ 7.6

Question 16

A manufacturer wants to increase the absorption capacity of a sponge. Based on past data, the average sponge could absorb 103.5ml. After the redesign, the absorption amounts of a sample of sponges were (in millilitres): 121.3, 109.2, 97.6, 103.5, 112.4, 115.3, 106.5, 112.4, 118.3, and 115.3. What is the decision rule at the 0.01 level of significance to test if the new design increased the absorption amount of the sponge?

Accepted Answer

A)  Do not reject null hypothesis if computed t is less than 2.580 
B)  Do not reject null hypothesis if computed t is less than 2.821 
C)  Reject null hypothesis if computed z is 1.96 or larger 
D)  Reject null hypothesis if computed t is less than 2.764 
E)  None of these statements are true

Question 17

If the alternative hypothesis states that μ > 6,700, what is the rejection region for the hypothesis test?

Accepted Answer

A)  Both tails 
B)  Lower tail 
C)  Upper tail 
D)  Center 
E)  None of these statements are true

Question 18

A manufacturer wants to increase the shelf life of a line of cake mixes. Past records indicate that the average shelf life of the mix is 216 days. After a revised mix has been developed, a sample of nine boxes of cake mix gave these shelf lives (in days): 215, 217, 218, 219, 216, 217, 217, 218 and 218. At the 0.025 level, has the shelf life of the cake mix increased?

Accepted Answer

A)  Yes, because computed t is greater than the critical value. 
B)  Yes, because computed t is less than the critical value. 
C)  No, because computed t lies in the region of acceptance. 
D)  No, because 217.24 is quite close to 216. 
E)  None of these statements are true.

Question 19

A random sample of size 15 is selected from a normal population. The population standard deviation is unknown. Assume that a two-tailed test at the 0.10 significance level is to be used. For what value of t will the null hypothesis be rejected?

Accepted Answer

A)  To the left of -1.282 or to the right of 1.282 
B)  To the left of -1.345 or to the right of 1.345 
C)  To the left of -1.761 or to the right of 1.761 
D)  To the left of -1.645 or to the right of 1.645 
E)  None of these statements are true

Question 20

The mean weight of newborn infants at a community hospital is 6.6 pounds. A sample of seven infants is randomly selected and their weights at birth are recorded as 9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6 pounds. Does this sample support the original claim? What is the decision for a statistical significant change in average weights at birth at the 5% level of significance?

Accepted Answer

A)  Fail to reject the null hypothesis and conclude the mean is 6.6 lb. 
B)  Reject the null hypothesis and conclude the mean is higher than 6.6 lb. 
C)  Reject the null hypothesis and conclude the mean is lower than 6.6 lb. 
D)  Cannot calculate because population standard deviation is unknown. 
E)  None of these statements are true

Exam 9: One-Sample Tests of a Hypothesis

A manufacturer claims that less than 1% of all his products do not meet the minimum government standards. A survey of 500 products revealed ten did not meet the standard.

It is claimed that in a bushel of peaches less than ten percent are defective. A sample of 400 peaches is examined and 50 are found to be defective. If α = 0.025, what will be the decision?

i. If the critical values of the test statistic z are ±1.96, they are the dividing points between the areas of rejection and non-rejection. Ii) The probability of a Type I error is also referred to as alpha. Iii) A Type I error is the probability of accepting a true null hypothesis.

i. The probability of a Type I error is also referred to as alpha. ii. A Type I error is the probability of accepting a true null hypothesis. iii. A Type I error is the probability of rejecting a true null hypothesis.

Based on the Nielsen ratings, the local CBS affiliate claims its 11:00 PM newscast reaches 41% of the viewing audience in the area. In a survey of 100 viewers, 36% indicated that they watch the late evening news on this local CBS station. What is your decision if α = 0.01?

What is the level of significance?

The mean weight of newborn infants at a community hospital is 6.6 pounds. A sample of seven infants is randomly selected and their weights at birth are recorded as 9.0, 7.3, 6.0, 8.8, 6.8, 8.4, and 6.6 pounds. Does this sample support the original claim? What is the alternate hypothesis?

If the alternative hypothesis states that μ > 6,700, what is the rejection region for the hypothesis test?

A random sample of size 15 is selected from a normal population. The population standard deviation is unknown. Assume that a two-tailed test at the 0.10 significance level is to be used. For what value of t will the null hypothesis be rejected?