Question

Recall that "very satisfied" customers give the XYZ-Box video game system a rating that is at least 42. Suppose that the manufacturer of the XYZ-Box wishes to use the random sample of 68 satisfaction ratings to provide evidence supporting the claim that the mean composite satisfaction rating for the XYZ-Box exceeds 42. (a) Letting µ represent the mean composite satisfaction rating for the XYZ-Box, set up the null hypothesis H0 and the alternative hypothesis Ha needed if we wish to attempt to provide evidence supporting the claim that µ exceeds 42. H0: µ 42 versus Ha: µ 42. (b) The random sample of 68 satisfaction ratings yields a sample mean of x⎯⎯=42.810. Assuming that σ equals 2.70, use critical values to test H0 versus Ha at each of α = .10, .05, .01, and .001. (Round your answer z.05 to 3 decimal places and other z-scores to 2 decimal places.) z = Rejection points z.10 z.05 z.01 z.001 Reject H0 with α = , but not with α = (c) Using the information in part (b), calculate the p-value and use it to test H0 versus Ha at each of α = .10, .05, .01, and .001. (Round your answers to 4 decimal places.) p-value = Since p-value = is less than ; reject H0 at those levels of α but not with α = . (d) How much evidence is there that the mean composite satisfaction rating exceeds 42? There is evidence.

Answer 1