A recent decision by the Food and Drug Administration will make it easier for cu

Question

A recent decision by the Food and Drug Administration will make it easier for customers to buy hearing aids without seeing a doctor. In the US as a whole, 3.6% of residents have a hearing difficulty. A local retailer is considering offering hearing tests. The retailer only wants to offer the services if the local percentage is more than the national percentage. However the retailer doesn't have the budget for a census of local residents 1. Give the appropriate null and alternative hypothesis. Refer to pie chart, calculate an appropriate test statistic The retailer is especially concerned about wasting resources on hearing test. (This would be a Type I Error) which significance level would reflect this concern? (Write either 10% or 1% Sketch the rejection region for this test a. b. c. 2. Based upon this test, should the retailer offer the hearing test? Yes or No

Explanation / Answer

here n=4498,

null hypothesis H0:P=0.036

alternate hypothesis H1:P>0.036

(a) we use z-test and z=(p-P)/SE(p)=(0.04-0.036)/sqrt(0.036*(1-0.036)/4498)=1.44

(b) here leve of significance should be uses as 1%

(c) rejecteion region would be Z>2.33

(2) since we accept the null hypothesis as calcuated z=1.44 is less than critical z=2.32, so retailer should not offere the hearing test.

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