Using R software language answer the following: You want to know how many people

Question

Using R software language answer the following:

You want to know how many people in the US like NFL, so you start a survey by yourself. After collecting the sample, you find among the 1000 people in the sample, 532 people claim they love NFL.

• If you want to show the at least half of the population like NFL, what alternative hypothesis you should come up with? Just use words to describe. (10 pts)

• Use prop.test() function to run the test. What is the p-value? Can you reject the null on 5% significance level? What about 1% significance level? (10 pts)

Explanation / Answer

Solution:-

p = 532/1000

p = 0.532

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis: P > 0.50

Alternative hypothesis: P < 0.50

Note that these hypotheses constitute a one-tailed test. The null hypothesis will be rejected only if the sample proportion is too small.

Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method, shown in the next section, is a one-sample z-test.

Analyze sample data. Using sample data, we calculate the standard deviation () and compute the z-score test statistic (z).

= sqrt[ P * ( 1 - P ) / n ]

= 0.01578

z = (p - P) /

z = 2.03

where P is the hypothesized value of population proportion in the null hypothesis, p is the sample proportion, and n is the sample size.

Since we have a one-tailed test, the P-value is the probability that the z-score is greater than 2.03.

Thus, the P-value = 0.0212

Interpret results. Since the P-value (0.0212) is less than the significance level (0.05), we cannot accept the null hypothesis.

At 1 % signifucance level

Interpret results. Since the P-value (0.0212) is greater than the significance level (0.01), we have to accept the null hypothesis.

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