Question

In: Statistics and Probability

Please show work and write clearly..some of these i can not see numbers or anytihng written...

Please show work and write clearly..some of these i can not see numbers or anytihng written correctly .

A national sports magazine believes that 38% of Americans said they were fans of baseball. A polling company claims more Americans are fans of baseball. A random sample of 400 people indicated that 176 were baseball fans. Use a 0.01 level of significance. Answer each of the following.

a. State the null and alternate hypothesis. Make sure to use the proper notation.

b. Identify the claim.

c. Which test will you use to test the claim? Left tailed, right-tailed or two tailed?

d. What is the sample proportion?

e. If the P-value is 0.0067, what decision can be made? Reject the null hypothesis or fail to reject the null hypothesis?

f. State the conclusion in words.

Expert Solution

Let be the true proportion of Americans that are fans of baseball. The polling company claims more Americans are fans of baseball (that is more than 38% as claimed by the sports magazine). That is the polling company claims that p>0.38. This owuld be the alternative hypothesis has it has one of ineuqalities

a. State the null and alternate hypothesis. Make sure to use the proper notation.

ans:

Note: The null hypothesis is also sometimes written as

b. Identify the claim.

The polling company claims more Americans are fans of baseball (that is more than 38% as claimed by the sports magazine

ans: The claim is, the proportion of Americans that are fans of baseball is significantly greater than 38%

c. Which test will you use to test the claim? Left tailed, right-tailed or two tailed?

The alternative hypothesis has ">". This means this is a right tailed test

ans: We will use right tailed test to test the claim

d. What is the sample proportion?

A random sample of 400 people indicated that 176 were baseball fans.

The sample proportion of Americans that are baseball fans is

ans: the sample proportion is 0.44

e. If the P-value is 0.0067, what decision can be made? Reject the null hypothesis or fail to reject the null hypothesis?

We have to use a 0.01 level of significance

We will reject the null hypothesis if the p-value is less than the significance level.

Here, the p-value is 0.0067 and it is less than 0.01. Hence we reject the null hypothesis.

ans: Reject the null hypothesis.

f. State the conclusion in words.

ans: There is sufficient evidence to support the claim that the proportion of Americans that are fans of baseball is significantly greater than 38%

orchestra answered 2 years ago

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