Question

Some have argued that throwing darts at the stock pages to decide which companies to invest in could be a successful​ stock-picking strategy. Suppose a researcher decides to test this theory and randomly chooses 100 companies to invest in. After 1​ year, 52 of the companies were considered​ winners; that​ is, they outperformed other companies in the same investment class. To assess whether the​ dart-picking strategy resulted in a majority of​ winners, the researcher tested H 0​: P = 0.5 versus H 1​: P>0.5 and obtained a​ P-value of 0.3446. Explain what this​ P-value means and write a conclusion for the researcher.​ (Assume alpha is 0.1 or​ less.)

Choose the correct explanation below.

A. About 52 in 100 samples will give a sample proportion as high or higher than the one obtained if the population proportion really is greater than 0.5.

B. About 34 in 100 samples will give a sample proportion as high or higher than the one obtained if the population proportion really is 0.5.

C. About 34 in 100 samples will give a sample proportion as high or higher than the one obtained if the population proportion really is greater than 0.5.

D. About 52 in 100 samples will give a sample proportion as high or higher than the one obtained if the population proportion really is 0.5.

Choose the correct conclusion below.

A. Because this probability is​ small, do not reject the null hypothesis. There is not sufficient evidence to conclude that the​ dart-picking strategy resulted in a majority of winners.

B. Because this probability is not​ small, do not reject the null hypothesis. There is not sufficient evidence to conclude that the​ dart-picking strategy resulted in a majority of winners.

C. Because this probability is​ small, reject the null hypothesis. There is sufficient evidence to conclude that the​ dart-picking strategy resulted in a majority of winners.

D. Because this probability is not​ small, reject the null hypothesis. There is sufficient evidence to conclude that the​ dart-picking strategy resulted in a majority of winners.

Answer 1

Answer)

Given P-Value = 0.3446 ~ 0.34

So answer here is

About 34 in 100 samples will give a sample proportion as high or higher than the one obtained if the population proportion really is 0.5.

That is it gives the value as extreme as possible when null hypothesis is really true

And we reject Null hypothesis Ho when p-value is small

As here p-value is large

So conclusion is

Because this probability is not​ small, do not reject the null hypothesis. There is not sufficient evidence to conclude that the​ dart-picking strategy resulted in a majority of winners.