1. On Monday SF Giants pitcher Matt Moore pitched 8 innings and threw 93 pitches of which 62 pitches were strikes.

(5) a. Construct a 99% confidence interval for the true proportion(π) of strikes.

(10) b. At the 10% level test the null hypothesis that the true proportion of strikes is greater than 0.60.

(5) c. What sample size is required if you wanted to be 95% sure that the true proportion of strikes to total pitches is within 1 percentage point.

2.A leading consumer magazine, The False Traders, claims that the small coffee sold at PHILZ coffee shop does not contain 12 ounces of coffee. A sample of 16 customers who purchased a small coffee yielded the following information:

– a sample mean equal to 11.90 ounces and a sample standard deviation of 0.16 ounces.

(5) a. Set up a 90% confidence interval for the true population mean?

(10) b. At the 5% level, test the hypothesis whether the true mean is less than 12 ounces.

3. The consumer magazine also claims that the cinnamon rolls at STARBUCKS do not weigh at least 8 ounces. A random sample of 25 customers purchasing cinnamon rolls yields the following results:

• the sample mean equals 7.87 ounces
• it is known from previous studies that the population standard deviation equals 0.25 ounces.

(5) a. Set up a 95% confidence interval for the true mean?

(5) b. What sample size is required if you want to be 99% sure that the sample mean will be within 0.2 ounces of the true mean?

(10) c. Test the hypothesis that the true population mean is less than 8 ounces. Set the type one error equal to 1%.