Math 1342 Review 4(answers)
1. A sample of 100 fifth graders are selected and given a math test. The sample average score is 62.7. Assume that the test scores of all fifth graders are normally distributed with a population standard deviation of 9.2. Construct confidence intervals for the population mean test score with the following confidence levels:
a) 90% b) 95% c) 99%
d) What happens to the width of confidence intervals as the confidence level increases?
2. A truck stop keeps extensive transaction records. If random samples are drawn of sales records with each showing average sales of 63.9 gallons of diesel fuel and each with sample standard deviation of 5.6 gallons, construct 95% confidence intervals for the mean number of gallons for the entire collection of records assuming the following sample sizes:
a) 15 b) 20 c) 25
d) What happens to the width of the confidence intervals as the sample size increases?
3. It is desired to estimate the average number of hours that teenagers spend watching TV per week. How large a sample is needed to estimate the mean to within ¼ hour with 99% confidence, if you assume that the population is normal with a population standard deviation of 3.2 hours?
4. In a sample survey, 140 of 500 persons interviewed in a large city said that they shop in the downtown area at least once a week. Construct confidence intervals for the proportion of people in the city who shop downtown at least once a week at the following confidence levels:
a) 90% b) 95% c) 99%
5. You want to estimate the proportion of all drivers who exceed 80 mph on a stretch of road between Houston and San Antonio. How large a sample will you need to take to be able to assert with probability .95 that the error of your estimate is at most .04?
6. A researcher wants to know what proportion of the lakes in the area contain hazardous pollution levels. He randomly selects 200 lakes and determines that 45 have hazardous levels of pollution.
a) Determine a 95% confidence interval for the population proportion.
b) If a local politician states that only 20% of the lakes are hazardously polluted, does the study provide evidence to contradict the politician’s view?
7. A random sample of size 1,000 produces a sample mean of 53.5 with a population standard deviation of 5.3. Test the hypotheses:
H0:
H1:
at the 5% level of significance.
8. A random sample of size 200 produces a sample mean of 4,117 with a population standard deviation of 300. Test the hypotheses:
H0:
H1:
at the 1% level of significance.
9. Researchers randomly select 12 vegetarian children that are 6 years old. The average height of the children is 42.5 inches with a sample standard deviation of 3.8 inches. The average height for all six-year-olds is 45.75 inches. Is there evidence at the 5% level of significance that six-year-old vegetarian children have a different mean height than the mean height of all six-year-old children?
10. For years, the percentage of passengers with one or more pieces of carry-on luggage has been stable at 38%. An airline recently selected 300 passengers at random and determined that 148 passengers had carry-on luggage. Is there evidence of an increase in carry-on luggage at the level of significance of 1%?