Problem: A school claims that the average IQ of their students is 98 with a standard deviation of 4. A random sample of 64 students is tested and found to have a mean IQ of 100. Use a 0.01 significance level.

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Illustrative Example: 1. A manufacturer of ropes has developed a new rope made of nylon that he claims to have a breaking strength of 25.2 kilograms with standard deviation of 2.3 kilograms. Test that hypothesis that u = 25.2 against the alternative that u #25.2 if a random sample of 48 pieces of ropes are tested and found to have a mean breaking strength of 24.7 kilograms. Use a 0.01 level of significance. Solutions: Steps in Hypothesis Testing Output 1. State the null hypothesis (H.) H =25.2 2. State the alternative hypothesis (H.). H #25.2 3. Determine the level of significance and the a = 0.01 critical regions. Critical Regions: z >2.575 and z