Question

1. According to a University Center for Logistics Management, 10% of all merchandise sold in the United States gets returned. A Seattle department store sampled 90 items sold in January and found that 10 of the items were returned.

If you have the following null and alternative hypotheses for a test you are running:

H0:p=0.1
Ha:p<0.1

Calculate the test statistic, rounded to 3 decimal places

2. Suppose you are testing the following claim: "Less than 72% of people support legalizing same sex marriage." Express the null and alternative hypotheses in symbolic form for a hypothesis test (enter as a percentage).

H0:p   (Enter percentages, not decimals. Example 99%, not 0.99)

H1:p (Enter percentages, not decimals. Example 99%, not 0.99)

Answer 1

Answer(1):

Number of items returned from sample= x= 10

Total sample size = n =90

The sample proportion is

p=x/n

p= 10/90

p= 0.1111

We have to test

H0: P=0.1

H1: P<0.1

The test statistic to test the above hypothesis is

The value of test statistic is 0.351.

Answer(2):

We have to test "Less than 72% of people support legalizing same sex marriage."

The null and alternative hypothesis can be given as below:

H0: p ≥ 72%
H1: p < 72%