Carry out a hypothesis test for a significant difference between the two population proportions, at significance level α = 0.05. The hypotheses being tested are: H 0: p 1 - p 2 = 0 H a: p 1 - p 2 ≠ 0. Complete the test by filling in the blanks in the following: An estimate of the difference in population proportions is . The standard error is (3 dec places). The distribution is (examples: normal / t12 / chisquare4 / F5,6). The test statistic has value TS= . Testing at significance level α = 0.05, the rejection region is: less than and greater than (2 dec places). There (is evidence/is no evidence) to reject the null hypothesis, H 0. There (is sufficient/is insufficient) evidence to suggest that there is a difference between the two population proportions, p 1 and p 2. ii) Estimate the difference in population proportions by calculating a 95% confidence interval. The difference between the population proportions, the proportion of population 1, p 1, minus the proportion of population 2, p 2, is estimated to be between and .
A company is carrying out a consumer satisfaction survey for two of its products, product A and product B. The company believes that product A receives a higher proportion of satisfied customers than product B. Out of the 80 product A customers surveyed, 52 said they were satisfied with the product and out of the 100 product B customers surveyed, 42 said they were satisfied with the product. Use these sample statistics to compare the proportion of product A customers that are satisfied, p 1, and the proportion of product B customers that are satisfied, p 2.
i) Carry out a hypothesis test for a significant difference between the two population proportions, at significance level α = 0.05.
The hypotheses being tested are:
H 0: p 1 - p 2 = 0
H a: p 1 - p 2 ≠ 0.
Complete the test by filling in the blanks in the following:
An estimate of the difference in population proportions is .
The standard error is (3 dec places).
The distribution is (examples: normal / t12 / chisquare4 / F5,6).
The test statistic has value TS= .
Testing at significance level α = 0.05, the rejection region is:
less than and greater than (2 dec places).
There (is evidence/is no evidence) to reject the null hypothesis, H 0.
There (is sufficient/is insufficient) evidence to suggest that there is a difference between the two population proportions, p 1 and p 2.
ii) Estimate the difference in population proportions by calculating a 95% confidence interval.
The difference between the population proportions, the proportion of population 1, p 1, minus the proportion of population 2, p 2, is estimated to be between and .
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
