In a random sample of visitors to a famous tourist attraction, 84 of 250 men and

Question

In a random sample of visitors to a famous tourist attraction, 84 of 250 men and 156 of 250 women bought souvenir. Let theta_1 be the true population proportion of men who bought souvenirs at this tourist attraction. Let theta_2 be the true population proportion of men who bought souvenirs at this tourist attraction. Construct a 92% confidence interval for the difference between the true proportions of men and women. theta_1 - theta_2, who buy souvenirs at this tourist attraction. Provide an interpretation of your confidence interval in part (a). Based on the interval obtained in part (a), is there evidence that the true proportion of women who buy souvenirs at this tourist attraction is larger than that of men? Why or Why not?

Explanation / Answer

Here we have to find 92% confidence interval for difference in proportion (1-2).

Given that,

x1 = 84

n1 = 250

x2 = 156 and

n2 = 250

c = confidence level = 92% = 0.92

We can find 92% confidence interval by using TI-83 calculator.

Steps :

STAT --> TESTS --> 8 : 2-PropZInt --> ENTER --> Input the values of x1, n1, x2, n2 and C-level --> Calculate --> ENTER

Output is,

92% confidence interval for 1-2 is (-0.3629, -0.2131).

Interpretation : We are 92% confident that the difference of population proportion is in between -0.3629 and -0.2131.

Proportion for men is 0.336 and proportion of female is 0.624 whic hdoes not lies in the interval.

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