According to the Pew Research Center, 14% of adults rate basketball as their fav

Question

According to the Pew Research Center, 14% of adults rate basketball as their favorite sport to watch. Your boss believes this proportion may be higher among adults under age 35, and wants you to collect evidence to see if this is true. Your boss is comfortable with the probability of a Type I error being 0.05. You survey 60 adults under age 35, and find that 23% of them rate basketball as their favorite sport. Conduct a hypothesis test and state your conclusion.sample proportion as p = 0.23,sample size as n = 60,The hypothesized proportion here is P = 0.14, The p-value here is 0.0488 < 0.05 which is the level of significance, therefore the test is significant and we can reject the null hypothesis. So we have sufficient evidence here that the proportion of adults rate basketball as their favorite sport to watch is higher than 0.14.

1)Since your firm will base some expensive decisions on the results of the previous hypothesis test, your boss decides that you need to be more conservative in how you draw conclusions. How would do this? Discuss how your conclusion might change.

Explanation / Answer

1) Science sets a conservative standard to meet for a researcher to claim that s/he has made a discovery of a real phenomenon. The standard is the alpha level, usually set of .05. Assuming that the null hypothesis is true, this means we may reject the null only if the observed data are so unusual that they would have occurred by chance at most 5 % of the time. The smaller the alpha, the more stringent the test (the more unlikely it is to find a statistically significant result).  

So, if we decrease alpha to let's say 0.01

p then > 0.01

Then, null cant be rejected. This would tell us that there is not sufficient evidence that the proportion of adults rate basketball as their favorite sport to watch is higher than 0.14.

And thus, company might not promote basketball that much in their stores or online.

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