Please help me with this problem Recall that \"very satisfied\" customers give t

Question

Please help me with this problem Recall that "very satisfied" customers give the XYZ-Box videogame system a rating that is at least 42. Suppose that themanufacturer of the XYZ-Box wished to use the random sample of 65satisfaction ratings to provide evidence supporting the claim thatthe mean composite satisfaction rating for the XYZ-Box exceeds42. a. Letting represent the mean compositsatisfaction rating for the XYZ- Box set up the null andalternative hypothese needed if we wish to attempt to provideevidence supporting the claim that exceeds 42. b. In the context of this situation, interpret making aType 1 error: interpret making a Type II error. Please help me with this problem Recall that "very satisfied" customers give the XYZ-Box videogame system a rating that is at least 42. Suppose that themanufacturer of the XYZ-Box wished to use the random sample of 65satisfaction ratings to provide evidence supporting the claim thatthe mean composite satisfaction rating for the XYZ-Box exceeds42. a. Letting represent the mean compositsatisfaction rating for the XYZ- Box set up the null andalternative hypothese needed if we wish to attempt to provideevidence supporting the claim that exceeds 42. b. In the context of this situation, interpret making aType 1 error: interpret making a Type II error.

Explanation / Answer

The null hypothesis is H0: = 42 The alternative hypothesis is HA: >42. A type I error is a "false positive". In other words, it isthe error of rejecting the null hypothesis when the null hypothesisis actually correct. In this problem, a Type I error occurswhen you reject the null hypothesis that the mean rating is 42,when in reality, the mean is greater than 42. A type II error is a "false negative". In other words, it isthe error of failing to reject the null hypothesis when it is infact not true. In this problem, a Type II error occurs whenyou do not reject the null hypothesis that the mean rating is 42(in other words, you assume that the rating is equal to 42), whenin reality, the mean is greater than 42.

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