1. For the following statement, write the null hypothesis and the alternative hypothesis. Also label which one is the claim. Company X claims that the average salary for an entry level employee is $35,000

2. A pizza restaurant manager claims that the average home delivery time for their pizza is no more than 18 minutes. A random sample of 36 home delivery pizzas was collected. The sample mean was found to be 19.25 minutes and the standard deviation was found to be 3.3 minutes. Is there evidence to reject the manager’s claim at alpha =.02? Perform an appropriate hypothesis test, showing the necessary calculations and/or explaining the process used to obtain the results.

3. At a jewelry store, the probability for a customer to make a purchase when entering the store is 35%. We asked 25 customers enter the store whether they made a purchase or not. (a) Is this a binomial experiment? Explain how you know. (b) Use the correct formula to find the probability that, out of 25 customers, exactly 10 of them make a purchase. Show your calculations or explain how you found the probability

4. The monthly utility bills are normally distributed with a mean value of $160 and a standard deviation of $25. (a) Find the probability of having a utility bill between 120 and 180. (b) Find the probability of having a utility bill less than $120. (c) Find the probability of having a utility bill more than $210

5. A Mall manager claims that in average every customer spends $52 per a single visit to the mall. To test this claim, you took a sample of 36 customers and found the sample mean to be $55 and the sample standard deviation to be $12. 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 60 businesses, he found the mean number of transaction per month to be 38 and the standard deviation to be 8.5 transactions. (a) Find a 95% 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. (Points : 20)

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. (Points : 20)

8. The ages of 10 students are listed in years:{ 17,22,19,24,21,23,29,18,22,28 } (a) Find the mean, median, mode, sample variance, and range. (b) Do you think that this sample might have come from a normal population? Why or why not?