# Statistics MCQs – Hypothesis testing for one population Part 5

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81. 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 is the value of the test statistic for the hypothesis test?

a. z = 3.73

b. t = 3.73

c. z = 0.75

d. t = 0.75

e. z = 2.98

Answer: D

82. 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 is the value of the test statistic for the hypothesis test?

a. z = 3.73

b. t = 3.73

c. z = 0.75

d. t = 2.98

e. z = 2.98

Answer: D

83. 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 value of the test statistic for this test?

a. z = -2.47

b. t = -2.47

c. z = 1.65

d. t = 1.65

e. z = 2.98

Answer: B

84. 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 value of the test statistic for this test?

a. z = -2.47

b. t = -2.47

c. z = 1.65

d. t = 1.65

e. z = 2.98

Answer: D

85. 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 value of the test statistic for this test?

a. z = -0.82

b. t = -0.82

c. z = -1.92

d. t = -1.92

e. z = 2.98

Answer: B

86. 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 value of the test statistic for this test?

a. z = -0.82

b. t = -0.82

c. z = -1.92

d. t = -1.92

e. z = 2.98

Answer: D

87. 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 value of the test statistic for this test?

a. z = -0.82

b. t = -0.82

c. z = -1.92

d. t = -1.92

e. t = 2.29

Answer: E

88. 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 value of the test statistic for this test?

a. 2.20

b. 1.41

c. 2.99

d. 1.80

e. 1.01

Answer: A

89. 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 value of the test statistic for this test?

a. 2.20

b. 1.41

c. 2.99

d. 1.80

e. 1.01

Answer: B

90. 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 value of the test statistic for this test?

a. 2.20

b. 1.41

c. 2.99

d. 1.80

e. 1.01

Answer: C

91. 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 value of the test statistic for this test?

a. 2.20

b. 1.41

c. 2.99

d. 1.80

e. 1.01

Answer: D

92. 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 value of the test statistic for this test?

a. 2.20

b. 1.41

c. 2.99

d. 1.80

e. 1.01

Answer: E

93. 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. What is the test statistic value for the hypothesis test that would test whether the mean number of cups of coffee drunk daily by students is different to 3.1?

a. t = 1.85

b. z = 1.85

c. t = -1.85

d. z = -1.85

e. t = 2.03

Answer: A

94. In a hypothesis test, the following random sample of six observations was selected from a normal distribution: 118, 105, 112, 119, 105, and 111. You are asked to conclude whether the population mean is different from 100 using the p-value method. What is the estimated p-value for this test?

a. p-value < 0.005

b. p-value < 0.010

c. p-value = 0.025

d. p-value = 0.010

e. p-value > 0.050

Answer: B

95. In a hypothesis test, the following random sample of six observations was selected from a normal distribution: 98, 105, 112, 119, 105, and 111. You are asked to conclude whether the population mean is different from 100 using the p-value method. What is the estimated p-value for this test?

a. p-value < 0.005

b. p-value < 0.010

c. p-value = 0.025

d. p-value = 0.010

e. p-value < 0.050

Answer: E

96. In a hypothesis test, the following random sample of six observations was selected from a normal distribution: 118, 90, 112, 119, 105, and 111. You are asked to conclude whether the population mean is different from 100 using the p-value method. What is the estimated p-value for this test?

a. p-value < 0.100

b. p-value < 0.010

c. p-value = 0.025

d. p-value = 0.010

e. p-value < 0.050

Answer: A

97. In a hypothesis test, the following random sample of six observations was selected from a normal distribution: 118, 105, 102, 119, 105, and 111. You are asked to conclude whether the population mean is different from 100 using the p-value method. What is the estimated p-value for this test?

a. p-value < 0.005

b. p-value < 0.010

c. p-value < 0.020

d. p-value = 0.010

e. p-value > 0.050

Answer: C

98. In a hypothesis test, the following random sample of six observations was selected from a normal distribution: 118, 105, 112, 119, 85, and 111. You are asked to conclude whether the population mean is different from 100 using the p-value method. What is the estimated p-value for this test?

a. p-value < 0.005

b. p-value < 0.100

c. p-value = 0.025

d. p-value < 0.200

e. p-value > 0.050

Answer: D

99. A one sample, one-tail t-test is conducted and the test statistic value is calculated to be 2.56. The degrees of freedom for the test are 10. Which of the following conclusions for the test would be correct?

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

b. the null hypothesis can be rejected at the 1% 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 a and c above are correct conclusions

Answer: E

100. A one sample, one-tail t-test is conducted and the test statistic value is calculated to be 2.56. The degrees of freedom for the test are 45. Which of the following conclusions for the test would be correct?

a. the null hypothesis can be rejected at the 0.5% level of significance

b. the null hypothesis can be rejected at the 1% 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: E