# Statistics MCQs – Hypothesis testing for one population Part 6

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101. A one sample, one-tail t-test is conducted and the test statistic value is calculated to be 1.86. The degrees of freedom for the test are 16. Which of the following conclusions for the test would be correct?

a. the null hypothesis can be rejected at the 1% level of significance

b. the null hypothesis can be rejected at the 2.5% level of significance

c. the null hypothesis can be rejected at the 5% level of significance

d. both a and b above are correct conclusions

e. both b and c above are correct conclusions

Answer: C

102. The recommended daily dietary allowance for zinc among males older than age 50 years is 15 mg/day. A study undertaken on a sample of 115 males aged between 65 and 74 years reports the average daily intake as 11.3 mg with a standard deviation of 6.43 mg. Researchers with to test whether the actual average daily zinc intake of males aged between 65 and 74 years falls below the recommended allowance. What is the conclusion of the test in this case?

a. p < 0.005, we therefore reject H_{0} and conclude that the daily zinc intake of males between 65 and 74 is less than the recommended daily allowance

b. p < 0.005, we therefore cannot reject H_{0} and conclude that the daily zinc intake of males between 65 and 74 is less than the recommended daily allowance

c. p > 0.05, we therefore cannot reject H_{0}, and conclude that the daily zinc intake of males between 65 and 74 equals the recommended daily allowance

d. p > 0.05, we therefore accept the alternative hypothesis, and conclude that the daily zinc intake of males between 65 and 74 is less than the recommended daily allowance

e. p < 0.005, we therefore reject H_{0} and conclude that the daily zinc intake of males between 65 and 74 is the same as the recommended daily allowance

Answer: A

103. The recommended daily dietary allowance for zinc among males older than age 50 years is 15 mg/day. A study undertaken on a sample of 115 males aged between 65 and 74 years reports the average daily intake as 12.3 mg with a standard deviation of 6.43 mg. Researchers with to test whether the actual average daily zinc intake of males aged between 65 and 74 years falls below the recommended allowance. What is the conclusion of the test in this case?

a. p < 0.005, we therefore reject H_{0} and conclude that the daily zinc intake of males between 65 and 74 is less than the recommended daily allowance

b. p < 0.005, we therefore cannot reject H_{0} and conclude that the daily zinc intake of males between 65 and 74 is less than the recommended daily allowance

c. p > 0.05, we therefore cannot reject H_{0}, and conclude that the daily zinc intake of males between 65 and 74 equals the recommended daily allowance

d. p > 0.05, we therefore accept the alternative hypothesis, and conclude that the daily zinc intake of males between 65 and 74 is less than the recommended daily allowance

e. p < 0.005, we therefore reject H_{0} and conclude that the daily zinc intake of males between 65 and 74 is the same as the recommended daily allowance

Answer: A

104. The recommended daily dietary allowance for zinc among males older than age 50 years is 15 mg/day. A study undertaken on a sample of 115 males aged between 65 and 74 years reports the average daily intake as 13.3 mg with a standard deviation of 6.43 mg. Researchers with to test whether the actual average daily zinc intake of males aged between 65 and 74 years falls below the recommended allowance. What is the conclusion of the test in this case?

a. p < 0.005, we therefore reject H_{0} and conclude that the daily zinc intake of males between 65 and 74 is less than the recommended daily allowance

b. p < 0.005, we therefore cannot reject H_{0} and conclude that the daily zinc intake of males between 65 and 74 is less than the recommended daily allowance

c. p > 0.05, we therefore cannot reject H_{0}, and conclude that the daily zinc intake of males between 65 and 74 equals the recommended daily allowance

d. p > 0.05, we therefore accept the alternative hypothesis, and conclude that the daily zinc intake of males between 65 and 74 is less than the recommended daily allowance

e. p < 0.005, we therefore reject H_{0} and conclude that the daily zinc intake of males between 65 and 74 is the same as the recommended daily allowance

Answer: A

105. The recommended daily dietary allowance for zinc among males older than age 50 years is 15 mg/day. A study undertaken on a sample of 115 males aged between 65 and 74 years reports the average daily intake as 14.3 mg with a standard deviation of 6.43 mg. Researchers with to test whether the actual average daily zinc intake of males aged between 65 and 74 years falls below the recommended allowance. What is the conclusion of the test in this case?

_{0} and conclude that the daily zinc intake of males between 65 and 74 is less than the recommended daily allowance

_{0} and conclude that the daily zinc intake of males between 65 and 74 is less than the recommended daily allowance

_{0}, and conclude that the daily zinc intake of males between 65 and 74 equals the recommended daily allowance

_{0} and conclude that the daily zinc intake of males between 65 and 74 is the same as the recommended daily allowance

Answer: C

106. The recommended daily dietary allowance for zinc among males older than age 50 years is 15 mg/day. A study undertaken on a sample of 115 males aged between 65 and 74 years reports the average daily intake as 12.9 mg with a standard deviation of 6.43 mg. Researchers with to test whether the actual average daily zinc intake of males aged between 65 and 74 years falls below the recommended allowance. What is the conclusion of the test in this case?

_{0} and conclude that the daily zinc intake of males between 65 and 74 is less than the recommended daily allowance

_{0} and conclude that the daily zinc intake of males between 65 and 74 is less than the recommended daily allowance

_{0}, and conclude that the daily zinc intake of males between 65 and 74 equals the recommended daily allowance

_{0} and conclude that the daily zinc intake of males between 65 and 74 is the same as the recommended daily allowance

Answer: A

107. The mean life of a battery used in a digital clock is 305 days. The lives of the batteries follow a normal distribution. The battery was recently modified to last longer. A sample of 20 of the modified batteries had a mean life of 311 days with a standard deviation of 12 days. A hypothesis test is undertaken to determine whether the modification increased the battery life. What conclusion can be made about the battery life, given a 5% level of significance for the test?

a. we do not reject the null hypothesis at the 5% level of significance and conclude that the mean battery life has increased

b. we reject the null hypothesis at the 5% level of significance and conclude that the mean battery life has not increased

c. we do not reject the null hypothesis at the 5% level of significance and conclude that the mean battery life has not increased

d. we reject the null hypothesis at the 5% level of significance and conclude that the mean battery life has increased

e. no conclusion can be made about the mean battery life as too little information is available

Answer: D

108. The mean life of a battery used in a digital clock is 305 days. The lives of the batteries follow a normal distribution. The battery was recently modified to last longer. A sample of 20 of the modified batteries had a mean life of 308 days with a standard deviation of 12 days. A hypothesis test is undertaken to determine whether the modification increased the battery life. What conclusion can be made about the battery life, given a 5% level of significance for the test?

a. we do not reject the null hypothesis at the 5% level of significance and conclude that the mean battery life has increased

b. we reject the null hypothesis at the 5% level of significance and conclude that the mean battery life has not increased

c. we do not reject the null hypothesis at the 5% level of significance and conclude that the mean battery life has not increased

d. we reject the null hypothesis at the 5% level of significance and conclude that the mean battery life has increased

e. no conclusion can be made about the mean battery life as too little information is available

Answer: C

109. The mean life of a battery used in a digital clock is 305 days. The lives of the batteries follow a normal distribution. The battery was recently modified to last longer. A sample of 20 of the modified batteries had a mean life of 315 days with a standard deviation of 12 days. A hypothesis test is undertaken to determine whether the modification increased the battery life. What conclusion can be made about the battery life, given a 5% level of significance for the test?

a. we do not reject the null hypothesis at the 5% level of significance and conclude that the mean battery life has increased

b. we reject the null hypothesis at the 5% level of significance and conclude that the mean battery life has not increased

c. we do not reject the null hypothesis at the 5% level of significance and conclude that the mean battery life has not increased

d. we reject the null hypothesis at the 5% level of significance and conclude that the mean battery life has increased

e. no conclusion can be made about the mean battery life as too little information is available

Answer: D

110. The mean life of a battery used in a digital clock is 305 days. The lives of the batteries follow a normal distribution. The battery was recently modified to last longer. A sample of 20 of the modified batteries had a mean life of 307 days with a standard deviation of 12 days. A hypothesis test is undertaken to determine whether the modification increased the battery life. What conclusion can be made about the battery life, given a 5% level of significance for the test?

e. no conclusion can be made about the mean battery life as too little information is available

Answer: C

111. The mean life of a battery used in a digital clock is 305 days. The lives of the batteries follow a normal distribution. The battery was recently modified to last longer. A sample of 20 of the modified batteries had a mean life of 313 days with a standard deviation of 12 days. A hypothesis test is undertaken to determine whether the modification increased the battery life. What conclusion can be made about the battery life, given a 5% level of significance for the test?

e. no conclusion can be made about the mean battery life as too little information is available

Answer: D

112. The eating disorder Bulimia Nervosa has been linked to the level of self-esteem of the sufferer. Before receiving treatment, self-esteem scores were obtained from a random sample of 21 sufferers and the following statistics were calculated: sample mean = 22.3 and sample standard deviation = 5.0. You wish to test whether or not the mean self-esteem score differs from 25 using a 5% significance level. What is the approximate p-value for this test?

a. 0.01 < p-value < 0.025

b. 0.02 < p-value < 0.05

c. 0.05 < p-value < 0.10

d. 0.10 < p-value < 0.20

e. p-value > 0.2

Answer: B

113. The eating disorder Bulimia Nervosa has been linked to the level of self-esteem of the sufferer. Before receiving treatment, self-esteem scores were obtained from a random sample of 21 sufferers and the following statistics were calculated: sample mean = 26.8 and sample standard deviation = 5.0. You wish to test whether or not the mean self-esteem score differs from 25 using a 5% significance level. What is the approximate p-value for this test?

a. 0.01 < p-value < 0.025

b. 0.02 < p-value < 0.05

c. 0.05 < p-value < 0.10

d. 0.10 < p-value < 0.20

e. p-value > 0.2

Answer: D

114. The eating disorder Bulimia Nervosa has been linked to the level of self-esteem of the sufferer. Before receiving treatment, self-esteem scores were obtained from a random sample of 21 sufferers and the following statistics were calculated: sample mean = 24.1 and sample standard deviation = 5.0. You wish to test whether or not the mean self-esteem score differs from 25 using a 5% significance level. What is the approximate p-value for this test?

a. 0.01 < p-value < 0.025

b. 0.02 < p-value < 0.05

c. 0.05 < p-value < 0.10

d. 0.10 < p-value < 0.20

e. p-value > 0.2

Answer: E

115. The eating disorder Bulimia Nervosa has been linked to the level of self-esteem of the sufferer. Before receiving treatment, self-esteem scores were obtained from a random sample of 21 sufferers and the following statistics were calculated: sample mean = 22.9 and sample standard deviation = 5.0. You wish to test whether or not the mean self-esteem score differs from 25 using a 5% significance level. What is the approximate p-value for this test?

a. 0.01 < p-value < 0.025

b. 0.02 < p-value < 0.05

c. 0.05 < p-value < 0.10

d. 0.10 < p-value < 0.20

e. p-value > 0.2

Answer: C

116. The eating disorder Bulimia Nervosa has been linked to the level of self-esteem of the sufferer. Before receiving treatment, self-esteem scores were obtained from a random sample of 21 sufferers and the following statistics were calculated: sample mean = 27.5 and sample standard deviation = 5.0. You wish to test whether or not the mean self-esteem score differs from 25 using a 5% significance level. What is the approximate p-value for this test?

a. 0.01 < p-value < 0.025

b. 0.02 < p-value < 0.05

c. 0.05 < p-value < 0.10

d. 0.10 < p-value < 0.20

e. p-value > 0.2

Answer: B

117. 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 42.78 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: B

118. 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 41.78 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: D

119. 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 43.78 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: A

120. 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 42.28 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: C