STAT 200 WEEK 6 HW

 Lane et al.

18. Find the probability that the sum of the 100 values falls between the numbers you found in and .

20. Find the sum with a z–score of 0.5.

7. In words, define the random variables X and X ¯ .

13. Identify the following:

a. x ¯ = ______

b. σ = ______

c. n = ______

65. Previously, an organization reported that teenagers spent 4.5 hours per week, on average, on the phone. The organization

thinks that, currently, the mean is higher. Fifteen randomly chosen teenagers were asked how many hours per week they

spend on the phone. The sample mean was 4.75 hours with a sample standard deviation of 2.0. Conduct a hypothesis test.

The null and alternative hypotheses are:

a. Ho: x ¯ = 4.5, Ha : x ¯ > 4.5

b. Ho: μ ≥ 4.5, Ha: μ < 4.5

c. Ho: μ = 4.75, Ha: μ > 4.75

d. Ho: μ = 4.5, Ha: μ > 4.5

71. Previously, an organization reported that teenagers spent 4.5 hours per week, on average, on the phone. The organization

thinks that, currently, the mean is higher. Fifteen randomly chosen teenagers were asked how many hours per week they

spend on the phone. The sample mean was 4.75 hours with a sample standard deviation of 2.0. Conduct a hypothesis test,

the Type I error is:

a. to conclude that the current mean hours per week is higher than 4.5, when in fact, it is higher

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

c. to conclude that the mean hours per week currently is 4.5, when in fact, it is higher

d. to conclude that the mean hours per week currently is no higher than 4.5, when in fact, it is not higher

77. An article in the San Jose Mercury News stated that students in the California state university system take 4.5 years, on

average, to finish their undergraduate degrees. Suppose you believe that the mean time is longer. You conduct a survey of

49 students and obtain a sample mean of 5.1 with a sample standard deviation of 1.2. Do the data support your claim at the

1% level?

80. At Rachel’s 11th birthday party, eight girls were timed to see how long (in seconds) they could hold their breath in a

relaxed position. After a two-minute rest, they timed themselves while jumping. The girls thought that the mean difference

between their jumping and relaxed times would be zero. Test their hypothesis.

Relaxed time (seconds) Jumping time (seconds)

26 21

47 40

30 28

22 21

Table 10.24

91. A powder diet is tested on 49 people, and a liquid diet is tested on 36 different people. Of interest is whether the liquid

diet yields a higher mean weight loss than the powder diet. The powder diet group had a mean weight loss of 42 pounds

with a standard deviation of 12 pounds. The liquid diet group had a mean weight loss of 45 pounds with a standard deviation

of 14 pounds.

121. A local cancer support group believes that the estimate for new female breast cancer cases in the south is higher in

2013 than in 2012. The group compared the estimates of new female breast cancer cases by southern state in 2012 and in

2013. The results are in Table 10.32.