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 70 satisfaction ratings to provide evidence supporting the claim that the mean composite satisfaction rating for the XYZ-Box exceeds 42. Letting mu represent the mean composite satisfaction rating for the XYZ-Box. set up the null hypothesis H_0 and the alternative hypothesis H_a needed if we wish to attempt to provide evidence supporting the claim that mu exceeds 42 The random sample of 70 satisfaction ratings yields a sample mean of x = 42.830 Assuming that o equas 2.63. use critical values to test H_0 versus H_a at each of alpha =.10. 05..01. and 001. (Round your answer z.05 to 3 decimal places and other z-scores to 2 decimal places Using the information in part (b). calculate the p-value and use it to test H_0 versus H_a at each of sigma = 10..05..01. and.001. (Round your answers to 4 decimal places.) How much evidence is the-e that the mean composite satisfaction rating exceeds 42? There is very strong evidence.

Explanation / Answer

a)

Formulating the null and alternative hypotheses,              
              
Ho:   u   <=   42  
Ha:    u   >   42   [ANSWER]

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b)

Getting the test statistic, as              
              
X = sample mean =    42.83          
uo = hypothesized mean =    42          
n = sample size =    70          
s = standard deviation =    2.63          
              
Thus, z = (X - uo) * sqrt(n) / s =    2.64040997 [ANSWER]

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Using table/technology,

z(0.10) = 1.28
z(0.05) = 1.645
z(0.01) = 2.33
z(0.001) = 3.09 [ANSWERS]

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hence, we reject Ho at [[0.10, 0.05, 0.01]] but not at [[0.001]]. [ANSWER]

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c)

Also, the p value is              
              
p =    0.00414029   [ANSWER]

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Since   P value is less than [[0.10, 0.05, 0.01]]: Reject Ho at those levels but not at [[0.0001]].

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d)

There is very strong evidence. [ANSWER]

[Hi! It depends on the convention you use in class. Since we rejected it at 0.01 level, it is somehow "strong", in that sense.]

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