Answer:
Null Hypothesis, : or
Alternate Hypothesis, : or
Yes, normal sampling distribution can be used.
Step-by-step explanation:
We are given that the sample statistics are from independent random samples. Claim: = , alpha(α) = 0.10 Sample statistics: =59, =171 and =36, = 203
We have to test the claim about the difference between two population proportions and at the given level of significance alpha(α) using the given sample statistics.
Let = population proportion of first group
= population proportion of second group
SO, Null Hypothesis, : or
Alternate Hypothesis, : or
The test statistics that will be used here is <u>Two-sample z proportion</u> statistics;
T.S. = ~ N(0,1)
where, = = sample proportion of first group
= = sample proportion of second group
= sample size of first group = 171
= sample size of second group = 203
So, Yes here normal sampling distribution can be used because the proportion test is approximately followed by a normal z distribution.