Question

The number of successes and the sample size for a simple random sample from a population are given below. X-7, 6-35. H:p=0.4, H:p<0.42-001 a. Determine the sample proportion b. Decide whether using the one-proportion z test is appropriate c. If appropriate, use the one-proportion z test to perform the specified hypothesis test. Click here to view a table of areas under the standard normal curve for negative values of z. c. Determine the test statistic, if appropriate Select the correct choice below if necessary, fill in the answer box to complete your answer A z- (Round to two decimal places as needed) OB. The one proportion test is not appropriate

Answer 1

Sample proportion, pcap = 7/35 = 0.2

one proportion z-test

Below are the null and alternative Hypothesis,
Null Hypothesis: p = 0.4
Alternative Hypothesis: p < 0.4

Rejection Region
This is left tailed test, for α = 0.01
Critical value of z is -2.33.
Hence reject H0 if z < -2.33

Test statistic,
z = (pcap - p)/sqrt(p*(1-p)/n)
z = (0.2 - 0.4)/sqrt(0.4*(1-0.4)/35)
z = -2.42

P-value Approach
P-value = 0.0078
As P-value < 0.01, reject the null hypothesis.