Question

When people turn to for news is different for various age groups. Suppose that a study conducted on this issue was based on 200 respondents who were between between the ages of 36 and 50, and 200 respondents who were above 50. Of the 200 respondents who were between 36 and 50, 82 got their news primarily from newspapers. Of the 200 respondents who were above age 50, 104 got their news primarily from newspapers.

a. Construct 2×2 contingency table.

b. Is there evidence of a significant difference in the proportion who get their news primarily from the newspapers between those 36 to 50 years old and those above 50 years old? Given the level of significance is 0.05.

c. Determine the p-value in (b) and interpret the meaning.

Please provide excel formulas and detailed explanations. ( I am a beginner in regards to statistics.)

Thank you in advance.

Answer 1

a)

The 2×2 contingency table for the respondents of two age groups who got their news primarily from newspapers and not news primarily from newspapers is,

		Newspaper
		Yes	No
Age (in years)	36-50	82	118
	>50	104	96

b)

Since we are comparing two sample proportion, z-test for two population proportion will be used.

The hypothesis test is performed in following steps,

Step 1: The null and alternative hypothesis are,

Where, p1 is the proportion of age group 36-50 years who got their news primarily from newspapers and p2 is the proportion of age group more than 50 years who got their news primarily from newspapers

This is a two tailed test

Step 2: The significance level level,

Step 3: The z-statistic is obtained using the formula,

Where,

Now,

Step 4:

The P-value for the z-statistic is obtained from z distribution table for z = -2.205

In excel P-value is obtained using the function =NORM.S.DIST(z, cumulative)

The P-value for two tailed = 2 x P-value for two tailed = 2 x 0.0137 = 0.0275

Since the p-value is less than 0.05, the null hypothesis is rejected. Hence we can conclude that there is statistically significant difference between proportion of age group 36-50 years who got their news primarily from newspapers and proportion of age group more than 50 years who got their news primarily from newspapers

c)

Here, the P-value can be interpreted as, the probability of getting the difference in proportions more extreme when the null hypothesis is true such that if the p-value is less than significance level, reject the null hypothesis which means there is a significant difference in proportion