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. If testing the polling company's claim, state the hypothesis and identify which hypothesis represents the claim.

Answer: The alternative hypothesis represents the claim

Step-by-step explanation:

We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean

For the null hypothesis,

µ = 0.38

For the alternative hypothesis,

µ > 0.38

Considering the population proportion, probability of success, p = 0.38

q = probability of failure = 1 - p

q = 1 - 0.38 = 0.6

Considering the sample,

Sample proportion, P = x/n

Where

x = number of success = 176

n = number of samples = 400

P = 176/400 = 0.44

We would the test statistic which is the z score

z = (p - P) / √pq/n

z = (0.44 - 0.38) / √ (0.38 * 0.62) / 400 = 2.47

Recall, population proportion, P = 0.38

The difference between sample proportion and population proportion (P - p) is 0.44 - 0.38 = 0.06

Since the curve is symmetrical and it is a two tailed test, the p for the left tail is 0.38 - 0.06 = 0.32

the p for the right tail is 0.38 + 0.06 = 0.44

These proportions are higher and lower than the null proportion. Thus, they are evidence in favour of the alternative hypothesis. We will look at the area in both tails. Since it is showing in one tail only, we would double the area

From the normal distribution table, the area above z is 1 - 0.9932 = 0.0068

We would double this area to include the area in the left tail of z = - 2.47. Thus

p = 0.0068 * 2 = 0.014

Since alpha, 0.01 < than the p value, 0.014, then we would fail to reject the null hypothesis. Therefore, at a 1% level of significance, we do not have enough evidence to reject the null hypothesis