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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

Solution Summary

The solution provides step by step method for the calculation of test statistic for hypothesis testing problems . Formula for the calculation and Interpretations of the results are also included.

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