1. For the following statement, write the null hypothesis and the alternative hypothesis. Also label which one is the claim. A car manufacturer claims that their cars makes at least 35 miles per gallon of fuel.

2. A pizza restaurant manager claims that the average home delivery time for their pizza is no more than 20 minutes. A random sample of 49 home delivery pizzas was collected. The sample mean was found to be 21.25 minutes and the standard deviation was found to be 4.3 minutes. Is there evidence to reject the manager’s claim at alpha =.01? Perform an appropriate hypothesis test, showing the necessary calculations and/or explaining the process used to obtain the results.

3. A researcher found that 85% of customers who make purchase at a department store are pleased with the store customer service. We asked 20 customers whether or not they are please with the store customer service.

(a) Is this a binomial experiment? Explain how you know.

(b) Use the correct formula to find the probability that, out of 20 customers, exactly 12 of them are pleased with the store customer service. Show your calculations or explain how you found the probability.

4. The monthly utility bills are normally distributed with a mean value of $150 and a standard deviation of $20.

(a) Find the probability of having a utility bill between 135 and 170.

(b) Find the probability of having a utility bill less than $135.

(c) Find the probability of having a utility bill more than $180.

5. A Mall manager claims that in average every customer spends $42 per a single visit to the mall. To test this claim, you took a sample of 49 customers and found the sample mean to be $39 and the sample standard deviation to be $9. At alpha = 0.05, test the Mall’s manager claim. Perform an appropriate hypothesis test, showing the necessary calculations and/or explaining the process used to obtain the results.

6. A bank manager wanted to estimate the mean number of transactions businesses make per month. For a sample of 55 businesses, he found that mean number of transaction per month to be 32 and the standard deviation to be 7.5 transactions.

(a) Find a 90% confidence interval for the mean number of business transactions per month. Show your calculations and/or explain the process used to obtain the interval.

(b) Interpret this confidence interval and write a sentence that explains it.

7. A company’s CEO wanted to estimate the percentage of defective product per shipment. In a sample containing 600 products, he found 45 defective products.

(a) Find a 99% confidence interval for the true proportion of defective product. Show your calculations and/or explain the process used to obtain the interval.

(b) Interpret this confidence interval and write a sentence that explains it.