# Statistics MCQs – Hypothesis testing for one population Part 4

61. A hypothesis test is conducted to test whether the mean age of clients at a certain health spa is equal to 25 or not. It is known that the population standard deviation of clients at the spa is 10. 36 clients are randomly selected, and their ages recorded, with the sample mean age being 29.8. What is your decision, at the 5% level of significance, regarding the null hypothesis that the mean age is equal to 25?

a. reject the null hypothesis at the 5% level of significance and conclude that the mean age of clients at the spa is less than 25

b. reject the null hypothesis at the 5% level of significance and conclude that the mean age of clients at the spa is not equal to 25

c. reject the null hypothesis at the 5% level of significance and conclude that the mean age of clients at the spa is more than 25

d. do not reject the null hypothesis at the 5% level of significance and conclude that the mean age of clients at the spa is 25

e. do not reject the null hypothesis at the 5% level of significance and conclude that the mean age of clients at the spa is less than 25

Answer: B

62. According to a certain TV broadcast station, the average number of violent incidents shown per episode of a TV series is 7. A researcher believes that this has increased in the last few years. A random sample of 16 recent episodes is selected which produced a sample mean of 7.5 violent incidents. Assume that the number of violent incidents follows a normal distribution and that the population standard deviation is 1.2. What would be the conclusion of a hypothesis test, if we were to perform a hypothesis test at a 5% level of significance in order to test whether the researcher’s belief is accurate or not (assume that the null hypothesis states that there is no change in the average number of violent incidents shown per episode)?

a. We cannot reject the null hypothesis and conclude that the mean number of violent incidents per episode has not increased

b. We reject the null hypothesis and conclude that the mean number of violent incidents per episode has indeed increased

c. We reject the null hypothesis since the p-value is greater than 0.05

d. We cannot reject the null hypothesis since the p-value is less than 0.05

e. There is not enough information given for us to reach a conclusion

Answer: B

63. According to a certain TV broadcast station, the average number of violent incidents shown per episode of a TV series is 7. A researcher believes that this has increased in the last few years. A random sample of 16 recent episodes is selected which produced a sample mean of 6.5 violent incidents. Assume that the number of violent incidents follows a normal distribution and that the population standard deviation is 1.2. What would be the conclusion of a hypothesis test, if we were to perform a hypothesis test at a 5% level of significance in order to test whether the researcher’s belief is accurate or not (assume that the null hypothesis states that there is no change in the average number of violent incidents shown per episode)?

a. We cannot reject the null hypothesis and conclude that the mean number of violent incidents per episode has not increased

b. We reject the null hypothesis and conclude that the mean number of violent incidents per episode has indeed increased

c. We reject the null hypothesis since the p-value is greater than 0.05

d. We cannot reject the null hypothesis since the p-value is less than 0.05

e. There is not enough information given for us to reach a conclusion

Answer: A

64. According to a certain TV broadcast station, the average number of violent incidents shown per episode of a TV series is 7. A researcher believes that this has increased in the last few years. A random sample of 16 recent episodes is selected which produced a sample mean of 7.2 violent incidents. Assume that the number of violent incidents follows a normal distribution and that the population standard deviation is 1.2. What would be the conclusion of a hypothesis test, if we were to perform a hypothesis test at a 5% level of significance in order to test whether the researcher’s belief is accurate or not (assume that the null hypothesis states that there is no change in the average number of violent incidents shown per episode)?

a. We cannot reject the null hypothesis and conclude that the mean number of violent incidents per episode has not increased

b. We reject the null hypothesis and conclude that the mean number of violent incidents per episode has indeed increased

c. We reject the null hypothesis since the p-value is greater than 0.05

d. We cannot reject the null hypothesis since the p-value is less than 0.05

e. There is not enough information given for us to reach a conclusion

Answer: A

65. According to a certain TV broadcast station, the average number of violent incidents shown per episode of a TV series is 7. A researcher believes that this has increased in the last few years. A random sample of 16 recent episodes is selected which produced a sample mean of 7.7 violent incidents. Assume that the number of violent incidents follows a normal distribution and that the population standard deviation is 1.2. What would be the conclusion of a hypothesis test, if we were to perform a hypothesis test at a 5% level of significance in order to test whether the researcher’s belief is accurate or not (assume that the null hypothesis states that there is no change in the average number of violent incidents shown per episode)?

c. We reject the null hypothesis since the p-value is greater than 0.05

d. We cannot reject the null hypothesis since the p-value is less than 0.05

e. There is not enough information given for us to reach a conclusion

Answer: B

66. According to a certain TV broadcast station, the average number of violent incidents shown per episode of a TV series is 7. A researcher believes that this has increased in the last few years. A random sample of 16 recent episodes is selected which produced a sample mean of 6.9 violent incidents. Assume that the number of violent incidents follows a normal distribution and that the population standard deviation is 1.2. What would be the conclusion of a hypothesis test, if we were to perform a hypothesis test at a 5% level of significance in order to test whether the researcher’s belief is accurate or not (assume that the null hypothesis states that there is no change in the average number of violent incidents shown per episode)?

c. We reject the null hypothesis since the p-value is greater than 0.05

d. We cannot reject the null hypothesis since the p-value is less than 0.05

e. There is not enough information given for us to reach a conclusion

Answer: A

67. A social scientist claims that the average adult watches less than 26 hours of television per week. He collects data on 25 individuals’ television viewing habits and finds that their mean number of hours watching television was 22.4 hours. Assume the population standard deviation is known to be eight hours, and the significance level adopted is 1%. What is the conclusion based on the data above?

a. Since z < -z_{0.01} , we reject the null hypothesis and conclude that the social scientist is right

b. Since z < -z_{0.01} , we fail to reject the alternate hypothesis and conclude that the social scientist is right

c. Since z > -z_{0.01} , we fail to reject the null hypothesis and conclude that the social scientist’s claim cannot be proved

d. Since z < -z_{0.01} , we fail to reject the null hypothesis and conclude that the social scientist’s claim cannot be proved.

e. Since z > -z_{0.01} , we reject the alternate hypothesis and conclude that the social scientist is right

Answer: C

68. 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. What is the value of the test statistic in this case (rounded to 2 decimal places)?

a. 4.72

b. 2.81

c. 2.10

d. 3.40

e. 1.63

Answer: A

69. 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. What is the value of the test statistic in this case (rounded to 2 decimal places)?

a. 4.72

b. 2.81

c. 2.10

d. 3.40

e. 1.63

Answer: B

70. 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. What is the value of the test statistic in this case (rounded to 2 decimal places)?

a. 4.72

b. 2.81

c. 2.10

d. 3.40

e. 1.63

Answer: C

71. 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. What is the value of the test statistic in this case (rounded to 2 decimal places)?

a. 4.72

b. 2.81

c. 2.10

d. 3.40

e. 1.63

Answer: D

72. 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. What is the value of the test statistic in this case (rounded to 2 decimal places)?

a. 4.72

b. 2.81

c. 2.10

d. 3.40

e. 1.63

Answer: E

73. 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 value of the test statistic in this case?

a. t = -6.17

b. z = -6.17

c. t = -4.50

d. z = -4.50

e. t = -2.84

Answer: A

74. 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 value of the test statistic in this case?

a. t = -6.17

b. z = -6.17

c. t = -4.50

d. z = -4.50

e. t = -2.84

Answer: C

75. 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 value of the test statistic in this case?

a. t = -6.17

b. z = -6.17

c. t = -4.50

d. z = -4.50

e. t = -2.84

Answer: E

76. 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 value of the test statistic in this case?

a. t = -1.17

b. z = -1.17

c. t = -3.50

d. z = -3.50

e. t = -2.84

Answer: A

77. 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 value of the test statistic in this case?

a. t = -1.17

b. z = -1.17

c. t = -3.50

d. z = -3.50

e. t = -2.84

Answer: C

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

a. z = 2.24

b. t = 2.24

c. z = 1.12

d. t = 1.12

e. z = 2.05

Answer: B

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

a. z = 2.24

b. t = 2.24

c. z = 1.12

d. t = 1.12

e. z = 2.05

Answer: D

80. 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 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: B