# Statistics MCQs – Hypothesis testing for one population Part 8

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141. Dentists believe that 53% of the general population suffers from tooth decay. The makers of Toothy Grin Toothpaste believe that using their product reduces tooth decay, and in order to support their claim study a random sample of 2000 Toothy Grin users. It turns out that 1050 of these are suffering from tooth decay. The evidence is investigated to see whether these figures present enough evidence to indicate a decrease in tooth decay for the Toothy Grin users. What is the appropriate test statistic value for this test?

a. t = -0.45

b. z = -0.45

c. t = 1.12

d. z = 1.12

e. t = 1.79

Answer: B

142. Dentists believe that 53% of the general population suffers from tooth decay. The makers of Toothy Grin Toothpaste believe that using their product reduces tooth decay, and in order to support their claim study a random sample of 2000 Toothy Grin users. It turns out that 1085 of these are suffering from tooth decay. The evidence is investigated to see whether these figures present enough evidence to indicate a decrease in tooth decay for the Toothy Grin users. What is the appropriate test statistic value for this test?

a. t = -0.45

b. z = -0.45

c. t = 1.12

d. z = 1.12

e. t = 1.79

Answer: D

143. It is suspected that, in lower class suburbs, residents replace their cars less often than the national average. We know that nationally, the proportion of new cars is 27.1%. A researcher investigates through proper sampling and finds that 37 out of 155 cars belonging to residents in a lower class suburb were new. We wish to test whether the proportion of new cars in this lower class suburb is less than the national average. What is the calculated test statistic for the hypothesis test indicated above?

a. 0.905

b. –0.07

c. 0.07

d. –0.905

e. 2.510

Answer: D

144. A major videocassette rental chain is considering opening a new store in an area that currently does not have any such stores. The chain will open if there is evidence that more than 25% of households in the area are equipped with videocassette recorders (VCR’s). It conducts a telephone poll of 300 randomly selected households in the area and finds that 96 have VCR’s. A hypothesis test is conducted to establish whether the proportion of households in the area equipped with VCR’s is more than 25%. What is the test statistic value for this hypothesis test?

a. t = 2.80

b. z = 2.80

c. t = -2.80

d. z = -2.80

e. t = -1.40

Answer: B

145. A random sample of 200 observations exhibits 36 successes. We wish to test at the 1% significance level whether the true proportion of successes in the population is less than 24%. What is the test statistic value for this hypothesis test?

a. t = 1.99

b. t = -1.99

c. z = 1.99

d. z = -1.99

e. z = 0.99

Answer: D

146. Scientists think that robots will play a crucial role in factories in the next 20 years. Suppose that in an experiment to determine whether the use of robots to weave computer cables is feasible, a robot was used to assemble 500 cables. The cables were examined and there were 14 defectives. Human assemblers have a defect rate of 3% (0.03). We wish to test whether the proportion of defectives produced by robots is less than that of humans. What is the value of the test statistic for this hypothesis test?

a. t = -0.26

b. z = -0.26

c. t = 2.60

d. z = 0.26

e. t = 0.26

Answer: B

147. In a random sample of 400 electrical components, 88 are found to be defective. You wish to test the null hypothesis that the population proportion of defective components is 20% versus the alternative hypothesis that the population proportion is not 20%. You choose a significance level of 5%. What is your statistical decision in this case?

a. Reject H_{o} at the 5% significance level

b. Do not reject H_{o} at the 5% significance level

c. Decision cannot be made at a 5% significance level

d. Decision cannot be made because sample size is large

e. More information is needed in order to be able to complete the hypothesis test

Answer: B

148. In a random sample of 400 electrical components, 95 are found to be defective. You wish to test the null hypothesis that the population proportion of defective components is 20% versus the alternative hypothesis that the population proportion is not 20%. You choose a significance level of 10%. What is your statistical decision in this case?

a. Reject H_{o} at the 10% significance level

b. Do not reject H_{o} at the 10% significance level

c. Decision cannot be made at a 10% significance level

d. Decision cannot be made because sample size is large

e. More information is needed in order to be able to complete the hypothesis test

Answer: A

149. In a random sample of 400 electrical components, 100 are found to be defective. You wish to test the null hypothesis that the population proportion of defective components is 20% versus the alternative hypothesis that the population proportion is not 20%. You choose a significance level of 5%. What is your statistical decision in this case?

a. Reject H_{o} at the 5% significance level

b. Do not reject H_{o} at the 5% significance level

c. Decision cannot be made at a 5% significance level

d. Decision cannot be made because sample size is large

e. More information is needed in order to be able to complete the hypothesis test

Answer: A

150. In a random sample of 400 electrical components, 75 are found to be defective. You wish to test the null hypothesis that the population proportion of defective components is 20% versus the alternative hypothesis that the population proportion is not 20%. You choose a significance level of 5%. What is your statistical decision in this case?

a. Reject H_{o} at the 5% significance level

b. Do not reject H_{o} at the 5% significance level

c. Decision cannot be made at a 5% significance level

d. Decision cannot be made because sample size is large

e. More information is needed in order to be able to complete the hypothesis test

Answer: B

151. In a random sample of 400 electrical components, 72 are found to be defective. You wish to test the null hypothesis that the population proportion of defective components is 20% versus the alternative hypothesis that the population proportion is not 20%. You choose a significance level of 5%. What is your statistical decision in this case?

a. Reject H_{o} at the 5% significance level

b. Do not reject H_{o} at the 5% significance level

c. Decision cannot be made at a 5% significance level

d. Decision cannot be made because sample size is large

e. More information is needed in order to be able to complete the hypothesis test

Answer: B

152. It is claimed that 2% of the population in a specific village suffer from a certain rare eye disorder. However, the doctor in the village believes that the true proportion of sufferers is actually more than 2%. He randomly tests 500 people from the village and finds that 12 of them have the eye disorder. If he were to conduct a hypothesis test to test whether the true mean proportion of sufferers is equal to or more than 2%, what would the p-value of the test be?

a. 0.261

b. 0.005

c. 0.626

d. 0.027

e. 0.100

Answer: A

153. It is claimed that 2% of the population in a specific village suffer from a certain rare eye disorder. However, the doctor in the village believes that the true proportion of sufferers is actually more than 2%. He randomly tests 500 people from the village and finds that 18 of them have the eye disorder. If he were to conduct a hypothesis test to test whether the true mean proportion of sufferers is equal to or more than 2%, what would the p-value of the test be?

a. 0.261

b. 0.005

c. 0.626

d. 0.027

e. 0.100

Answer: B

154. It is claimed that 2% of the population in a specific village suffer from a certain rare eye disorder. However, the doctor in the village believes that the true proportion of sufferers is actually more than 2%. He randomly tests 500 people from the village and finds that 9 of them have the eye disorder. If he were to conduct a hypothesis test to test whether the true mean proportion of sufferers is equal to or more than 2%, what would the p-value of the test be?

a. 0.261

b. 0.005

c. 0.626

d. 0.027

e. 0.100

Answer: C

155. It is claimed that 2% of the population in a specific village suffer from a certain rare eye disorder. However, the doctor in the village believes that the true proportion of sufferers is actually more than 2%. He randomly tests 500 people from the village and finds that 16 of them have the eye disorder. If he were to conduct a hypothesis test to test whether the true mean proportion of sufferers is equal to or more than 2%, what would the p-value of the test be?

a. 0.261

b. 0.005

c. 0.626

d. 0.027

e. 0.100

Answer: D

156. It is claimed that 2% of the population in a specific village suffer from a certain rare eye disorder. However, the doctor in the village believes that the true proportion of sufferers is actually more than 2%. He randomly tests 500 people from the village and finds that 14 of them have the eye disorder. If he were to conduct a hypothesis test to test whether the true mean proportion of sufferers is equal to or more than 2%, what would the p-value of the test be?

a. 0.261

b. 0.005

c. 0.626

d. 0.027

e. 0.100

Answer: E

157. A random sample of 319 front-seat occupants involved in head-on collisions in a certain region resulted in 95 who sustained no injuries. We wish to use this sample data to test whether the true proportion of uninjured occupants in head-on collisions exceeds 0.25 or not. What would your conclusion be for this test of hypothesis, given a 5% significance level?

a. I would conclude that the true proportion of uninjured occupants in head-on collisions has increased

b. I would conclude that the true proportion of uninjured occupants in head-on collisions has decreased

c. I would conclude that the true proportion of uninjured occupants in head-on collisions has remained at 0.25

d. I would conclude that the there is too little information to make a correct decision

e. I would conclude that the sample size in this case is too small and therefore the results of the test cannot be trusted

Answer: A

158. A random sample of 319 front-seat occupants involved in head-on collisions in a certain region resulted in 100 who sustained no injuries. We wish to use this sample data to test whether the true proportion of uninjured occupants in head-on collisions exceeds 0.25 or not. What would your conclusion be for this test of hypothesis, given a 5% significance level?

a. I would conclude that the true proportion of uninjured occupants in head-on collisions has increased

b. I would conclude that the true proportion of uninjured occupants in head-on collisions has decreased

c. I would conclude that the true proportion of uninjured occupants in head-on collisions has remained at 0.25

d. I would conclude that the there is too little information to make a correct decision

e. I would conclude that the sample size in this case is too small and therefore the results of the test cannot be trusted

Answer: A

159. A random sample of 319 front-seat occupants involved in head-on collisions in a certain region resulted in 90 who sustained no injuries. We wish to use this sample data to test whether the true proportion of uninjured occupants in head-on collisions exceeds 0.25 or not. What would your conclusion be for this test of hypothesis, given a 5% significance level?

a. I would conclude that the true proportion of uninjured occupants in head-on collisions has increased

b. I would conclude that the true proportion of uninjured occupants in head-on collisions has decreased

c. I would conclude that the true proportion of uninjured occupants in head-on collisions has remained at 0.25

d. I would conclude that the there is too little information to make a correct decision

e. I would conclude that the sample size in this case is too small and therefore the results of the test cannot be trusted

Answer: C

160. A random sample of 319 front-seat occupants involved in head-on collisions in a certain region resulted in 85 who sustained no injuries. We wish to use this sample data to test whether the true proportion of uninjured occupants in head-on collisions exceeds 0.25 or not. What would your conclusion be for this test of hypothesis, given a 5% significance level?

d. I would conclude that the there is too little information to make a correct decision

Answer: C