statistic

1. (15 pts.) An Internet service provider sampled 535 customers, and finds that 64 of them experienced an interruption in high-speed service during the previous month.

(a)  Find a point estimate for the population proportion of all customers who experienced an interruption.

(b)  Construct a 82.5% confidence interval for the proportion of all customers who experienced an interruption.

(c)  The company’s quality control manager claims that no more than 10% of it’s customers experienced an interruption during the previous month. Does the confidence interval contradict this claim? Explain.

2. (20 pts.) A marketing research company reported that 67% of online searches used Google as the search engine. A network administrator wants to determine whether the percentage of searches that use Google is different in his company. He samples 411 searches and finds that 300 of them use Google. Use level of significance as 0.01 and p-value method.

(a) (5 pts.) State the appropriate null and alternative hypothesis.

(b) (10 pts.) Find test statistics and P-value.
(c) (5 pts.) State the conclusion.

3. (25 pts.) According to the Nielsen Company, the mean number of TV sets in a U.S. household was 2.24. Assume the standard deviation is 1.1. A sample of 85 households is drawn.

(a)  What is the probability that the sample mean number of TV sets is greater than 2? (b)  What is the probability that the sample mean number of TV sets is between 2.5 and 3?

(c)  Find the 60th percentile of the sample mean.

(d)  Would it be unusual for the sample mean to be less than 2?

(e)  Do you think it would be unusual for an individual household to have fewer than 2 TV sets? Explain. Assume the population is approximately normal.

4. (20 pts.) Suppose the scores, on a college entrance examination are normally distributed with a mean of 550 and a standard deviation of 100. A certain prestigious university will consider for admission only those applicants whose scores exceed the 90% of the distribution. Find the minimum score an applicant must achieve in order to receive consideration for admission to the university.

5. (20 pts.) The mean alkalinity level of water specimens collected from the Han River in Seoul, Korea, is 50 milligrams per liter. Consider a random sample of 100 sample water specimens collected from a tributary of the Han River. Suppose the sample mean and sample standard deviation of the alkalinity levels for the sample are 67.8 mpl , 14.4 mpl respectively. Is there sufficient evidence (at ) to indicate that the population mean alkalinity level of water in the tributary exceeds 50 mpl? Use P-value method.