Hypothesis Testing Four Problems

1) A company gets a sample of 64 customers (n=64) and calculates the sample mean(X bar) of customer spending per week to be $85. Assume the company has calculated the population standard deviation of customer spending to be o=$8 and that this variable is normally distributed , calculate the following:a) A 90% confidence interval estimate of the population mean ub) A 95% confidence interval estimate of the population mean uc) How would you explain the confidence interval you found in (a) to a news reporter who needs to report this on national television?2) A major cell phone service provider has determined that the number of minutes that its customers use their phone is normally distributed with a mean of 450 minutes and a standard deviation of 50 minutes. The company is thinking of offering a discount to those who use the phone for less than 250 mins. during a given month. Based on the available information, answer the ff.a) How many minutes does a person use when the standardized Z score equals -2, -1, 0,1 and 2?b) What percentage of current customers would be eligible for the discount?3) Information given:** The manager of a paint store wants to know whether paint per can averages 1 gallon** Population standard deviation of the paint weight o=0.02 gallons.** The manager takes a random sample of 50 paint cans(n=50)** He finds the sample mean to be (X bar)=0.995 gallons.a) State the Null and Alternative Hypotheses:b) At a 95% confidence level, test whether the null hypothesis is correct.4) If you use a 0.05 level of significance in a two-tail hypothesis test, what will you decide if the computed value of the test statistics is Z=2.21?