Testing of Hypothesis Problems
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1. Suppose that the scores of architects on a particular creativity test are normally distributed. What percentage of architects have z scores (a) above.10 (b0 below-10, (c) above .20, (d) below .20 (e) above 1.10, (f) below 1.10 (g) above -.10 (h) below -.10 ?
2. Suppose a candidate running for sheriff claims that she will reduce the average speed of emergency response to less that 30 minutes. ( 30 minutes is thought to be the average response time with the current sheriff.) There are no past records, so the actual standard deviation of such response times can not be determined. Thanks to this campaign, she is elected sheriff and careful records are now kept. The response times for the first month are 26,30,28,29,25,28,32,35,24,and 23 min.
Using the .05 significance level, did she keep her promise? (a) go through the five steps of the hypothesis testing (b) Illustrate your answer with a histogram of the sample's scores and sketches of the population distribution and the distribution of means, showing the t score and cutoff points for significance. (c) explain your answer to someone who has never taken a course in statistics.
3. Compute a chi-square test for goodness of fit for each of the following, using the .05 level for each. In each problem, the expected distribution is equal frequencies in each category.
a. 5 10 5
b. 10 15 10
c. 10 20 10
d. 5 15 5
4. A sample of scores on an examination given to both males and females in a 4th grade class is:
Males 3,2,4,1,1,3,1,3,3,1,2,3,3,3,3,2,1,3,2,3
Females 4,1,4,1,2,3,1,3,3,1,2,3,2,3,1,2,1,3,2,1
At the 0.02 level of significance, is the mean grade of the female students higher than that of the males?
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Solution Summary
The solution gives step by step procedure for the calculation of students t test, z test and chi -square test. Null hypothesis, alternative hypothesis, critical value, p value and test statistics are given with interpretations.
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