Hypothesis testing problems

1.A researcher collects infant mortality data from a random sample of villages in a certain country. It is claimed that the average death rate in this country is the same as that of a neighboring country, which is known to be 17 deaths per 1000 live births. To test this claim using a test of hypotheses, what should the null and alternative hypotheses be?

2.The distribution of times that a company's technicians take to respond to trouble calls is normal with mean μ and standard deviation σ = 0.25 hours. The company advertises that its technicians take an average of no more than 2 hours to respond to trouble calls from customers. We wish to conduct a test to assess the amount of evidence against the company's claim. In a random sample of 25 trouble calls, the average amount of time that technicians took to respond was 2.1 hours. From these data, the P-value of the appropriate test is?

3.A local teachers' union claims that the average number of school days missed due to illness by the city's school teachers is fewer than 5 per year. A random sample of 28 city school teachers missed an average of 4.5 days last year, with a sample standard deviation of 0.9 days. Assume that days missed follow a normal distribution with mean μ. A test conducted to see whether there is evidence to support the union's claim will have a P-value of?

4.Jamaal, a player on a college basketball team, made only 50% of his free throws last season. During the off-season, he worked on developing a softer shot in the hope of improving his free-throw accuracy. This season, Jamaal made 54 of 95 free throws. Can we conclude that Jamaal's free-throw percentage p this season is significantly different from last year's percentage? The approximate P-value for an appropriate test is?

5.Which of the following would have no effect on the P-value of a z test for a population proportion p?
a) increasing the sample size
b) decreasing the significance level of the test, α
c) getting a different value of the sample proportion from the sample data
d) changing the null hypothesis

6. As part of a promotion for a new type of cracker, free samples are offered to shoppers in a local supermarket. The probability that a shopper will buy a package of crackers after tasting the free sample is 0.2. Different shoppers can be regarded as independent trials. Let be the sample proportion of the next n shoppers that buy a packet of crackers after tasting a free sample. How large should n be so that the standard deviation of is no more than 0.01?
a)4
b)16
c)64
d)1600