# The null hypothesis and the alternative hypothesis

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 25 minutes. A random sample of 49 home delivery pizzas was collected. The sample mean was found to be 26.5 minutes and the standard deviation was found to be 4 minutes. Is there evidence to reject the manager’s claim at alpha =.05? 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 \$130 and a standard deviation of \$15. (a) Find the probability of having a utility bill between 100 and 150. (b) Find the probability of having a utility bill less than \$90. (c) Find the probability of having a utility bill more than \$160.

5. A Mall manager claims that in average every customer spends \$37 per a single visit to the mall. To test this claim, you took a sample of 64 customers and found the sample mean to be \$34 and the sample standard deviation to be \$5. 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.

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