Discuss the below:
Q1. Suppose that the shoe company Alta Claims that their mean weekly sales are $17,350. A random sample of 35 weeks yields a sample mean of $10,450. With a sample standard deviation of s =$1500.
Given that the pair of hypothesis that correspond to the claim are
H0: µ = 17,350
H1: µ ≠ 17,350
Find the critical value for the hypothesis test. Assume that the significance level is α = 0.08.
Q2. Suppose that an insurance agent for State Ranch claims that the average life insurance policy premium that he sells is $450 per year. A sample of 40 customers yields a mean of x =$475 and a standard deviation of s = $85. You decide to test his claim at the α = 0.05 significance level.
If the hypothesis are
H0: µ = 450
H1: µ ≠ 450
With critical values of ±1.96, compute the sample statistic, and choose the appropriate conclusion.
Q3. Suppose that the company CEO for Quitters, Inc. claims that the average severance package for an employee at his company is $450,000. You decide to test his claim using a significance level of α = 0.04. A sample of 40 employees yields a mean of x = $414,845 with a sample standard deviation of s = $125,575. First, you set up your hypothesis as follows
H0: µ = $450,000 (claim)
H1: µ = $450,000
Compute the probability of getting a sample statistic at least as extreme as z = -1.77, and interpret this probability value.
Q4. Suppose a private university claims that more than 2/3 of their students graduate within for years. A random survey of 300 alumni finds that 190 of them graduated within 4 years.
Given that the pair of hypothesis that corresponds to the claim are
H0: p ≤ 0.67
H1: p ? 0.67
Find the critical value for the hypothesis test. Assume the significance level is α = 0.01.
Remember that this is a right-tailed test, so your critical value will be positive. Remember also that in one-tailed test, you don't have to cut your α-value in half.
Q5. Suppose that an insurance agent for Almost Heaven insurance claims that less than 20% of his life insurance policies ever have to ‘pay out'. You decide to test his claim at the α = 0.02 significance level. A sample of 75 policies from the last year finds that 30 of them had to pay out.
If the hypothesis are
H0: p ≥ 0.20
H1: p < 0.20
With a critical value of -2.05, compute the sample statistic, and choose the appropriate conclusion.
Q6. Suppose that the CEO of U-Store-it claims that more than 2/3 of his employees carry secondary health insurance. You decide to test his claim using a significance level of α = 0.05. A sample of 150 employees finds that 108 of them carry secondary health insurance.
First, you set up your hypothesis as follows:
H0: p ≤ 0.67
H1: p > 0.67(claim)
Compute the probability of getting a sample statistic as least as extreme as z = 1.30, and interpret this probability value. Remember that in one -tailed test such as this, you do not need to multiply your p-value by two.