**QUESTION**

**ANSWER**

63. Ans. **(d) p > 0.30**

We will state null hypothesis as – The proportion of girls who smoked to stay thin is 0.30. Hence, the alternate hypothesis will be – The proportion of girls who smoked to stay thin is more than 0.30.

65. Ans. **(d) H**_{0}**: µ = 4.5, H**_{a}**: µ > 4.5**

The organization wants to prove that the mean hours spent per week is greater than 4.5, and it was earlier 4.5 hours per week. Hence, the null hypothesis will be – The mean hours spent on phone per week by teenagers is 4.5; whereas the alternate hypothesis will be – The mean hours spent on phone per week by teenagers is more than 4.5.

69. Ans. **(c) less than 20%, when in fact, it is at least 20%**

In this question, the hypotheses will be as –

H_{0}: p __>__ 0.20 (The proportion of EVC students who attended the midnight showing of Harry Potter is greater than or equal to 20%.)

H_{a}: p < 0.20 (The proportion of EVC students who attended the midnight showing of Harry Potter is less than 20%.)

Type I error is defined as rejecting the null hypothesis, even when it is in fact true.

71. Ans. **(b) to conclude that the current mean hours per week is higher than 4.5, when in fact, it is the same**

For this experiment, we would take our hypotheses as –

H_{0}: µ = 4.5, H_{a}: µ > 4.5

Type 1 error, i.e. Alpha, is defined as rejecting the null hypothesis (H_{0}) when it is in fact true.

Putting all the values in our hypothesis, we would get the result.

75. Ans. **The data supports the claim at the 5% level.**

The solution is as follows: –

- H
_{0}: The mean age when smokers first start smoking is at least 19 years. (µ__>__19). - H
_{a}: The mean age when smokers first start smoking is less than 19 years. (µ < 19). - Significance Level, α = 0.05.
- Let be the mean age at which a smoker starts to smoke for the first time.
- The distribution is a normal distribution.
- z = – 2.71
- p-value = 0.0034
- As p-value is less than the significance level, we reject the null hypothesis.
- Conclusion – The mean age when smokers first start smoking is less than 19 years. (µ < 19).
- Confidence Interval = [17.45,18.76]

77. Ans. **The data supports the claim at the 1% level.**

The solution is as follows: –

- H
_{0}: The mean time taken by California state university students to complete their undergraduate degree is less than or equal to 4.5. (µ__<__4.5). - H
_{a}: The mean time taken by California state university students to complete their undergraduate degree is more than 4.5. (µ > 4.5). - Significance Level, α = 0.01.
- Let be the average time to finish an undergraduate degree.
- The distribution is a student’s-t distribution.
- t = 3.5
- p-value = 0.0005
- As p-value is less than the significance level, we reject the null hypothesis.
- Conclusion – The mean time taken by California state university students to complete their undergraduate degree is more than 4.5. (µ > 4.5).
- Confidence Interval = [4.755,5.445]

79. Ans. We have two subscripts here – 1. two-year colleges, 2. four-year colleges

The solution is as follows: –

- H
_{0}: The mean enrolment in four-year colleges is less than or equal to that in two-year colleges. (μ_{1}≥ μ_{2}). - H
_{a}: The mean enrolment in four-year colleges is greater than that in two-year colleges. (μ_{1}< μ_{2}). - Let be the difference between the mean enrolment of the two-year and four-year colleges.
- The distribution is a student’s-t distribution.
- Test statistic = – 0.2480
- p-value = 0.4019
- As p-value is greater than the significance level, we fail to reject the null hypothesis.
- Conclusion – There is not enough evidence to prove that the mean enrolment in four-year colleges is greater than that in two-year colleges.

93. Ans. We have two subscripts here – 1. California State Universities, 2. Private Universities

The solution is as follows: –

- H
_{0}: The average time taken by California State Universities students to graduate is less than or equal to those by private universities students. (μ_{1}__<__μ_{2}). - H
_{a}: The average time taken by California State Universities students to graduate is less than or equal to those by private universities students. (μ_{1}> μ_{2}). - Let be the difference between the mean time for graduation for California State Universities students and private universities students.
- The distribution is a normal distribution.
- Test statistic, z = 2.14
- p-value = 0.0163
- For significance level of 5%, p-value is less than the significance level, we will reject the null hypothesis.
- Conclusion – The average time taken by California State Universities students to graduate is less than or equal to those by private universities students.

99. Ans. We have two subscripts here – 1. Local, 2. National

The solution is as follows: –

- H
_{0}: The proportion of drug use in local seniors is less than or equal to those for national seniors. (p_{1}__<__p_{2}). - H
_{a}: The proportion of drug use in local seniors is greater than those for national seniors. (p_{1}> p_{2}). - Let p
_{1}– p_{2}be the difference between the difference in the proportions of local seniors and national seniors. - The distribution is a normal distribution for two proportions.
- Test statistic = 0.73
- p-value = 0.2326
- For significance level of 5%, p-value is greater than the significance level, we fail to reject the null hypothesis.
- Conclusion – The proportion of drug use in local seniors is less than or equal to those for national seniors

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