Recall that \"very satisfied\" customers give the XYZ-Box video game system a ra

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 63 satisfaction ratings to provide evidence supporting the claim that the mean composite satisfaction rating for the XYZ-Box exceeds 42.

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.

Using the information in part (b), calculate the p-value and use it to test H0 versus Ha at each of = .10, .05, .01, and .001. (Round your answers to 4 decimal places.)

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 63 satisfaction ratings to provide evidence supporting the claim that the mean composite satisfaction rating for the XYZ-Box exceeds 42.

Explanation / Answer

a) Hypothesis:

H0: µ 42 versus Ha: µ > 42.

b)

x = 42.850 , n =63 , s = 2.62

z = ( x- mean) / (s / sqrt(n))

= ( 42.850 - 42) / ( 2.62 / sqrt(63))

= 2.575

c) p value is calculated using z = 2.575

p value at 0.10 = 0.0050

  p value at 0.05 = 0.0050.

  p value at 0.01 = 0.0050.

Reject Ho at 0.10, 0.01 , 0.05

  p value at 0.001 = 0.0050.

We fail to reject H0 at 0.001

d)

There is sufficient evidence that the mean composite satisfaction rating exceeds 42

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