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How to Reduce Budget

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9.2.
The Federal Reserve Board is meeting to decide if it should reduce interest rates in order to stimulate economic growth. State the null and alternative hypotheses regarding economic growth that the board would formulate to guide its decision.

9.6.
A random sample is obtained from a population with variance σ2=625, and the sample mean is computed. Test the null hypothesis H0:μ=100 versus the alternative hypothesis H1:μ>100 with a=0.05. compute the critical value xc and state your decision rule for the following options: a. sample size n=25 b. sample size n=16 c. sample size n=44 d. sample size n=32

9.10.
A random sample of n=25 is obtained from a population with variance σ2, and the sample mean is computed to be x=70. Consider the null hypothesis H0:μ=80 versus the alternative hypothesis H1:μ<80. Compute the p-value for the following options: a. The population variance is σ2=225. b. The population variance is σ2=900. c. The population variance is σ2=400. d. The population variance is σ2=600.

9.13.
A pharmaceutical manufacturer is concerned that the impurity concentration in pills should not exceed 3%. It is known that from a particular production run impurity concentrations follow a normal distribution with a standard deviation of 0.4%. A random sample of 64 pills from a production run was checked, and the sample mean impurity concentration was found to be 3.07%. a. Test at the 5% level the null hypothesis that the population mean impurity concentration is 3% against the alternative that it is more than 3%. b. Find the p-value for this test. c. Suppose that the alternative hypothesis had been two-sided, rather than one-sided, with the null hypothesis H0:μ=3. State, without doing the calculations, whether the p-value of the test would be higher than, lower than, or the same as that found in part (b).

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