Test the following claim. Identify the null hypoyhesis, test statistic, critical

Question

Test the following claim. Identify the null hypoyhesis, test statistic, critical value (s), conclusion about the null hypothosis, and the final conclusion that addresses the original claim.

Test of older baseballs showed that when dropped 23 ft onto a concrete surface, they bounced an average of 230.8 cm. In a test of 45 new baseballs, the bounce heights had a mean of 238.4 cm. Assume that the standard devation of bounce heights is 3.8 cm. Use a 0.05 significance level to test the claim that the new baseballs have bounce heights with a mean different from 230.8 cm. Are the baseballs different?

• What are the null and alternative hypotheses?

• What is the value of the test statistic? Z = ________
(round to 2 decimals)

• Identify the critical value(s) of Z. Z = _______
(round to 2 decimals and use comma to separate answers as needed)

Explanation / Answer

Ho:(Null) Mu(new)= 230.8 Ha:(Alt) Mu(new) =/230.8 Z= (238.4-230.8)/3.8/sqrt45 Z=13.42 Critical value z= 1.96 (.05 level) Since test statistic is greater than the critical value we reject the null hypothesis and say there is evidence to support the hypothesis that the mean is different from 230.8.

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