1.(1) The claim by a weight loss Company is that on average, the client will lose 10 pounds over
first 2 weeks. 50 people who joined the programme are sampled, their weight loss is 9 pounds with a standard deviation of 2.8 pounds. Can we conclude at the .05 level that a person joining the programme will lose less than 10 pounds?
(2) The following is a random sample of 90-day futures prices in dollars for 1 troy oz. of silver from The Wall Street Journal issues in May and June of 1997: 4.74, 4.77, 4.87, 4.91, 4.83, 4.72, 4.92, 4.86, 4.97, 4.71, 4.90, 4.93, 4.75, 4.88, 4.79, 4.83, 4.89.
a. Calculate the mean
c. Standard deviation of the 90-day future price of silver data
(3) A mining company needs to estimate the average amount of copper ore per ton mined. A random sample of 50 tons gives a sample mean of 146,75 pounds. The population standard deviation is assumed to be 35.2 pounds.
a. Give a 95% confidence interval for the average amount of copper in the population of tons mined.
b. Give a 90% confidence interval for the average amount of coper per ton
c. Give a 99% confidence interval for the average amount of coper per ton
(4) An e-commerce Website gets 2,385 visitors on a particular day. Among these, 1790 visitors explore the products by looking at more pages at the site. Among these 1790 visitors who explore the products, 387 make a purchase.
a. If a visitor chosen at random from all those who visited the site, what is the probability that the visitor explored the products
b. If a visitor is chosen at random from all those who visited the site, what is the probability that the visitor made a purchase.
c. If a visitor is chosen at random from all those who explored the products, what is the probability that the visitor made a purchase.
d. Which of the preceding three probabilities is relevant to the design of the home page that leads to product page.
2.Weight loss: In a study to determine whether counseling could help people lose weight, a sample of people experienced a
eople experienced a group-based behavioral intervention, which involved weekly meetings with a trained interventionist for a period of six months. The following data are the numbers of pounds lost for 14 people, based on means and standard deviations given in the article. Assume the population is approximately normal. Perform a hypothesis test to determine whether the mean weight loss is greater than 20 pounds. Use the =α0.10 level of significance and the critical value method.
22.5 28.5 7.6 24.1 21.5 12.9 17.3
21.2 37.6 33.8 12.1 36.3 24.1 19.4