1. The number of successes and the sample size are given for a simple random sample from a population. Decide whether using the one-proportion z-test is appropriate.
x = 3, n = 80, H0: p = 0.04, Ha: p > 0.04
Use the two-proportions z-interval procedure to obtain the required confidence interval for the difference between two population proportions. Assume that independent simple random samples have been selected from the two populations.
2. A survey of students at one college found that 57 of 96 randomly selected freshmen and 85 of 118 randomly selected sophomores lived off campus. Find a 98% confidence interval for the difference between the proportions of freshmen and sophomores at this college who live off campus.
-0.278 to 0.025
0.468 to 0.721
-0.254 to 0.721
0.444 to 0.744
Use the one-proportion z-interval procedure to find the required confidence interval.
3. In a sample of 713 patients who underwent a certain type of surgery, 22% experienced complications. Find a 90% confidence interval for the proportion of all those undergoing this surgery who experience complications.
0.2045 to 0.2355
0.2001 to 0.2399
0.1892 to 0.2508
0.1945 to 0.2455
Find the P-value for the indicated hypothesis test.
4. In a sample of 47 adults selected randomly from one town, it is found that 9 of them have been exposed to a particular strain of the flu. Find the P-value for a hypothesis test to determine whether the proportion of all adults in the town that have been exposed to this strain of the flu differs from 8%.
Find the required sample size without making a guess for the observed value of .
5. A manufacturer wishes to estimate the proportion of washing machines leaving the factory that are defective. Obtain a sample size that will ensure a margin of error of at most 0.014 for a 97% confidence interval.