# Problems relating to confidence intervals and P values

1) In a survey conducted to determine the cost of vacations, 64 individuals were randomly sampled. Each person was asked the cost of her or his most recent vacation and the sample mean was computed as $1810.16. Assuming that the population standard deviation is $400, estimate with 95% confidence the average cost of all vacations.

2) The label on 4-litre cans of paint states that the amount of paint in the can is sufficient to paint 400 square feet. However, this number is quite variable. In fact, the amount of coverage is known to be approximately normally distributed with a standard deviation of 25 square feet. How large a sample should be taken to estimate the true mean coverage of all 4-litre cans to within 5 square feet with 95% confidence?

3) A random sample of 18 young men (20-30 years old) was sampled. Each person was asked how many minutes of sports they watched on television daily. The sample mean was 81.9 minutes. It is known that ? = 10. Test to determine at the 5% significance level whether there is enough statistical evidence to infer that the mean amount of television sports watched daily by all young adult men is greater than 50 minutes.

4) The campus bookstore reported that students paid an average of $267 per semester for textbooks. To verify this statement, the student union decided to select a random sample of students, and found the following amounts, in dollars, spent for textbooks:

321 286 290 330 310 250 270 280 299 265 291 275 281

At the .01 level of significance, can the student union conclude that the average amount spent on textbooks has increased? What is the p-value?

5) Many ski centres base their projections of revenues and profits on the assumption that the average skier skies 4 times per year. To investigate the validity of this assumption, a random sample of 63 skiers is drawn and each is asked to report the number of times they skied the previous year. The sample mean was found to be 4.84 times. If it assumed that the standard deviation is 2, can it be inferred at the 10% significance level that the assumption is wrong?

#### Solution Summary

The solution provides detailed explanations how to find out the confidence intervals and P values.