In each of Exercises, we have provided the numbers of successes and the sample sizes for independent simple random samples from two populations. In each case, do the following tasks. a.Determine the sample proportions.b.Decide whether using the two-proportions z-procedures is appropriate. If so, also do parts (c) and (d).c.Use the two-proportions z-test to conduct the required hypothesis test.d.Use the two-proportions z-interval procedure to find the specified confidence interval. x1 = 30, n1 = 80, x2 = 15, n2 = 20; two-tailed test, a = 0.05; 95% confidence interval
In each of Exercises, we have provided the numbers of successes and the sample sizes for independent simple random samples from two populations. In each case, do the following tasks.
a.Determine the sample proportions.
b.Decide whether using the two-proportions z-procedures is appropriate. If so, also do parts (c) and (d).
c.Use the two-proportions z-test to conduct the required hypothesis test.
d.Use the two-proportions z-interval procedure to find the specified confidence interval.
x1 = 30, n1 = 80, x2 = 15, n2 = 20; two-tailed test, a = 0.05; 95% confidence interval
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a.
The number of successes is x1=30, x2=15, the sample sizes for independent simple random samples from two populations are n1=80, n2=20, the test is a two-tailed test, α=0.05 and 90% confidence interval.
Sample proportion:
The fraction of the number of members sampled which have a specified attribute and the sample size n is termed as the sample proportion.
It is given that, x1 = 30, n1 = 80. Thus, p1 = 30/80 = 0.375.
Also, x2 = 15, n2 = 20. Thus, p2 = 15/20 = 0.75.
Thus, the sample proportions are p1 = 0.375 and p2 = 0.75.
b.
Two–Proportion z-test Procedure:
It is used to perform the hypothesis test for comparing two population proportion, p1 and p2.
Assumptions:
- Samples should be simple random samples.
- Samples should be independent.
- x1, n1−x1, x2 and n2−x2 should be equal to 5 or greater.
x1=30>5
n1− x1=80-30=50>5
Also,
x2=15>5
n2− x2=20-15=5≥5
Here, all the assumptions are satisfied therefore the two-proportion z-test procedure is appropriate.
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