Question 1. Assume the population has a normal distribution and the number of observations in a random sample is greater than fifty. If a z test is used to test a null hypothesis about the population mean versus the alternative that the true mean is greater than that specified by the null hypothesis, what is the critical value for a one-tailed test? Assume the type one-error rate is 0.05.
Question 2. Assume x is a random variable with mean μ and standard deviation σ. Find expressions for the mean and standard deviation of y if this variable is determined by the expression y = 4x +5. (Every value of x is modified by first being multiplied by 4 and then increased by 5.
Question 3. Assume normality and use the information given to find the p-value. Based on the p-value estimated, determine if the null hypothesis should be rejected at a 0.1 significance level. Select the correct answer if the test statistic in a "two-tailed test" is z= -1.63. Follow the procedure shown in Business Statistics.
a. p-value = 0.9484; fail to reject the null hypothesis
b. p-value = 0.0516; reject the null hypothesis
c. p-value = 0.0516; fail to reject the null hypothesis
d. p-value = 0.0258; reject the null hypothesis