# Statistics MCQs – Hypothesis testing for one population Part 7

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121. The owner of a petrol station wants to investigate the purchasing habits of motorists at his station. He takes a random sample of 28 motorists and finds that their average purchase is 41.28 litres of petrol with a standard deviation of 6.7 litres. He wishes to test whether the average fuel (petrol) purchase is more than 40 litres. What is the approximate p-value for this test?

a. p-value < 0.005

b. 0.01 < p-value < 0.025

c. 0.025 < p-value < 0.05

d. 0.05 < p-value < 0.10

e. p-value > 0.10

Answer: E

122. According to a coffee research organisation, the average student drinks 3.1 cups of coffee per day. A random sample of 12 students were interviewed and their sample mean was 3.425 with a standard deviation of 0.607. We wish to investigate whether the data suggests that the amount of coffee consumed is different to 3.1 cups daily, assuming a 5% level of significance. Which of the following is a suitable conclusion to the hypothesis test?

a. Since our test statistic lies in the rejection region we reject the null hypothesis at the 5% significance level and conclude that there is a difference

b. Since our test statistic does not lie in the rejection region we cannot reject the null hypothesis at the 5% significance level and conclude that there is no difference

c. Since the p-value is greater than the critical value we can reject the null hypothesis at the 5% significance level and conclude that there is a difference

d. Since the p-value is less than the critical value we cannot reject the null hypothesis at the 5% significance level and conclude that there is no difference

e. None of the above conclusions is correct

Answer: B

123. In a random sample of 400 electrical components, 88 are found to be defective. If the hypothesis is that 20% of the components are defective, what is the value of the test statistic that would test this claim?

a. t = 1.000

b. z = 1.000

c. t = 1.875

d. z = 1.875

e. z = 2.500

Answer: B

124. In a random sample of 400 electrical components, 95 are found to be defective. If the hypothesis is that 20% of the components are defective, what is the value of the test statistic that would test this claim?

a. t = 1.000

b. z = 1.000

c. t = 1.875

d. z = 1.875

e. z = 2.500

Answer: D

125. In a random sample of 400 electrical components, 100 are found to be defective. If the hypothesis is that 20% of the components are defective, what is the value of the test statistic that would test this claim?

a. t = 1.000

b. z = 1.000

c. t = 1.875

d. z = 1.875

e. z = 2.500

Answer: E

126. In a random sample of 400 electrical components, 75 are found to be defective. If the hypothesis is that 20% of the components are defective, what is the value of the test statistic that would test this claim?

a. t = -1.000

b. z = -1.000

c. t = -0.625

d. z = -0.625

e. z = 2.500

Answer: D

127. In a random sample of 400 electrical components, 72 are found to be defective. If the hypothesis is that 20% of the components are defective, what is the value of the test statistic that would test this claim?

a. t = -1.000

b. z = -1.000

c. t = -0.625

d. z = -0.625

e. z = 2.500

Answer: B

128. 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 value of the test statistic be?

a. z = 0.64

b. t = 0.64

c. z = 2.56

d. t = 2.56

e. z = -0.32

Answer: A

129. 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 value of the test statistic be?

a. z = 0.64

b. t = 0.64

c. z = 2.56

d. t = 2.56

e. z = -0.32

Answer: C

130. 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 value of the test statistic be?

a. z = 0.64

b. t = 0.64

c. z = 2.56

d. t = 2.56

e. z = -0.32

Answer: E

131. 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 value of the test statistic be?

a. z = 1.92

b. t = 1.92

c. z = 1.28

d. t = 1.28

e. z = -0.32

Answer: A

132. 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 value of the test statistic be?

a. z = 1.92

b. t = 1.92

c. z = 1.28

d. t = 1.28

e. z = -0.32

Answer: C

133. 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 is the value of the appropriate test statistic in this case?

a. 1.97

b. 2.62

c. 1.33

d. 0.68

e. -0.61

Answer: A

134. 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 is the value of the appropriate test statistic in this case?

a. 1.97

b. 2.62

c. 1.33

d. 0.68

e. -0.61

Answer: B

135. 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 is the value of the appropriate test statistic in this case?

a. 1.97

b. 2.62

c. 1.33

d. 0.68

e. -0.61

Answer: C

136. 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 is the value of the appropriate test statistic in this case?

a. 1.97

b. 2.62

c. 1.33

d. 0.68

e. -0.61

Answer: D

137. A random sample of 319 front-seat occupants involved in head-on collisions in a certain region resulted in 75 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 is the value of the appropriate test statistic in this case?

a. 1.97

b. 2.62

c. 1.33

d. 0.68

e. -0.61

Answer: E

138. 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 1005 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 = -2.46

b. z = -2.46

c. t = -1.79

d. z = -1.79

e. t = 1.79

Answer: B

139. 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 1020 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 = -2.46

b. z = -2.46

c. t = -1.79

d. z = -1.79

e. t = 1.79

Answer: D

140. 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 1100 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 = -2.46

b. z = -2.46

c. t = -1.79

d. z = 1.79

e. t = 1.79

Answer: D