Garrison Keller claims the children of Lake Wobegon are above average. You take
ID: 3177871 • Letter: G
Question
Garrison Keller claims the children of Lake Wobegon are above average. You take a simple random sample of 9 children from Lake Wobegon and measure their intelligence with a Wechsler test and find the following scores: {116, 128, 125, 119, 89, 99, 105, 116, and 118}. The mean of this sample (x) is 112.8. We know Wechsler scores are scaled to be normally distributed with a mean of 100 and standard deviation of 15. Is this sample mean sufficiently different from a population mean of 100 to reject the null hypothesis of “no difference?” 11. The claim being made in the example is that the population has higher than average intelligence. The null hypothesis is the population has average intelligence. Since an average intelligence score is 100: (2pts)
a. H0: > 100
b. H0: = 100
c. H0: = 100
d. H0: < 100
12. The alternative hypothesis claims that the sample mean is different from the population mean. What is the alternative hypothesis? (2pts)
a. Ha: > 100
b. Ha: = 100
c. Ha: 100
d. Ha: 100
13. (Use Ha from question 12) When conducting the test, the significance level is set at alpha =.05. P-value = 0.048. This provides good evidence to: (2pts)
a. Fail to reject the H0
b. Reject the H0
14. (Follow up to question 13) Explain what the results of the hypothesis test means in context of the scores. (4 pts)
15. If you wrongly reject the Null, it is a: (2pts)
a. Type I error
b. Type II error
16. Based on question 13, what is your tolerance of error (i.e. what percentage of the time are you allowing to wrongly reject the null hypothesis? (2pts)
a. 5%
b. 95%
c. 99%
d. 1% 17.
(Use Ha from question 12) Now, when conducting the test, the significance level is set at alpha =.01. The P-value = 0.048. This provides good evidence to: (2pts)
a. Fail to reject the H0
b. Reject the H0
18. (Follow up to question 17), explain what the results of the hypothesis test means in context of the scores. (4 pts)
19. The alternative hypothesis claims the population has a higher than average intelligence. Therefore: (2pts)
a. Ha: > 100
b. Ha: < 100
c. Ha: = 100
d. Ha: > 100
20. (Use Ha from question 19) When conducting the test, the significance level is set at alpha =.05. P-value = 0.048. This provides good evidence to: (2pts)
a. Fail to reject the H0
b. Reject the H0
21. (Follow up to question 20) Explain what the results of the hypothesis test means in context of the scores. (4 pts)
Explanation / Answer
11)
c. H0: = 100
12)
c. Ha: 100
13)
b. Reject the H0
p value < alpha
14)
test statistic = x - mean / stanadard error
= (112 .8 - 100) / ( 15/ sqrt(9))
= 2.56
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