# Testing hypotheses based on a given data set

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The publisher of a sports magazine plans to offer new subscribers on of the three gifts: a sweatshirt coffee cup or pair of earrings with the logo of their favorite team In a sample of 500 new subscribers, selections made sweatshirts 183,coffe cup

175 and earrings 142 at the .05 significance level is there a preference for the gifts or should we conclude that the gifts are equally well liked?

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The solution contains detailed explanation of testing hypotheses using the five-step procedures.

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Solution. We can set up the null hypothesis H0 and the alternative hypothesis H1 as follows.

H0: The gifts are equally well liked

H1: The gifts are NOT equally well liked.

We have

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- BSc , Wuhan Univ. China
- MA, Shandong Univ.

###### Recent Feedback

- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
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