5.19 The Egyptian Revolution. A popular uprising that started on January 25, 201

Question

5.19 The Egyptian Revolution. A popular uprising that started on January 25, 2011 in Egypt led to the 2011 Egyptian Revolution. Polls show that about 69% of American adults followed the news about the political crisis and demonstrations in Egypt closely during the first couple weeks following the start of the uprising. Among a random sample of 30 high school students, it was found that only 17 of them followed the news about Egypt closely during this time.2 (a) Write the hypotheses for testing if the proportion of high school students who followed the news about Egypt is different than the proportion of American adults who did. (b) Calculate the proportion of high schoolers in this sample who followed the news about Egypt closely during this time. (c) Describe how to perform a simulation and, once you had results, how to estimate the p-value. (d) Below is a histogram showing the distribution of paim in 10,000 simulations under the null hypothesis. Estimate the p-value using the plot and determine the conclusion of the hypothesis test. 0.15 0.10 0.05 0 1.0 0.6 0.8 0.4 Bm

Explanation / Answer

Part a

Here, we have to use one sample z test for the population proportion. The null and alternative hypothesis for this test is given as below:

Null hypothesis: H0: The proportion of high school students who followed the news about Egypt is 69%.

Alternative hypothesis: Ha: The proportion of high school students who followed the new about Egypt is not 69%.

H0: p = 0.69 versus Ha: p 0.69

This is a two tailed test.

The test statistic formula for this test is given as below:

t = (P – p) / sqrt(pq/n)

Part b

We are given

x = 17

n = 30

Sample proportion = P = x/n = 17/30 = 0.566667

Part c

We will find the sample proportions for the sampling distributions and then find t value given as below:

t = (0.566667 – 0.69) / sqrt(0.69*0.31/30)

t = -1.46061

After finding t value we will take decision about the null hypothesis.

Part d

We have to find the p-value by using the excel or z-table.

P-value = 0.1441

P-value > = 0.05

So, we do not reject the null hypothesis.

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