Problem 1: Life span in Hawaii
Travel Magazine reported that among the US states, Hawaii is the one with the longest life span of residents, where the population mean life span is 77 years. A random sample of 20 obituary notices in the Honolulu Journal gave the following information about life span (in years) of Honolulu residents:
72 68 81 93 56 19 78 94 83 84
77 69 85 97 75 71 86 47 66 88
Assuming that life span in Honolulu is normally distributed; does this information indicate that the mean life span for all Honolulu residents is less than 77 years? Do you have enough evidence to say that Travel magazine's report is not accurate? Use a 5% level of significance.
1) What type of hypothesis test is needed? What distribution should be used? Why?
2) State the two hypotheses here.
Ho : H1 :
3) Find the critical value and the test statistics. State them here.
4) Is this a right, left, or two-tailed test? Sketch a normal curve, mark the critical value and test statistics, and shade the rejection region on the curve.
5) Use your calculator to find the P value. State it here.
6) Do we reject or not reject the null hypothesis? Does this information indicate that the mean life span for all Honolulu residents is less than 77 years? Include the test statistics or P value in your discussion.
Problem 2: Critical Job Skills
In August 2011, 59% of employed adults in the United States reported that basic mathematical skills were critical or important to their job. The director of the Career Center at a 4-year college believes that this percentage has increased because of all the new technology use in the workplaces. In order to prove his point, he takes a random sample of 280 employed adults and finds that 65% of them feel that basic mathematical skills are critical or important to their job.
Is this enough evidence for the director to support his belief that more employed adults think that mathematical skills are important in their jobs? Use a 5% significance level.
1) What type of hypothesis test is needed? What distribution should be used? Why?
2) State the two hypotheses here.
Ho : H1 :
3) Find the critical value and the test statistics. State them here.
4) Is this a right, left, or two-tailed test? Sketch a normal curve, mark the critical value and test statistics, and shade the rejection region on the curve.
5) Use your calculator to find the P value. State it here.
6) Do we reject or not reject the null hypothesis? Is there sufficient evidence to conclude that the percentage of employed adults who feel basic mathematical skills are critical or very important to their job has increased? If you were the director, what kind of suggestions would you include in your report to your supervisor?
Problem 3: Too Much Salt?
The U.S. Food and Drug administration recommends 2400 mg daily allowance of sodium for children. A nutritionist claims that children under the age of 10 years are consuming more sodium than the recommended amount. To test her claim, she obtains a random sample of 110 children under the age of 10 years and measures their daily consumption of sodium. The mean amount of sodium consumed was found to be 2995 mg with a standard deviation of 1489 mg. The distribution of sodium amount is normal. Is this enough evidence to conclude that children under the age 10 consume significantly more sodium than the recommended amount? Use %5 significance level.
1) What type of hypothesis test is needed? What distribution should be used? Why?
2) State the two hypotheses here.
Ho : H1 :
3) Find the critical value and the test statistics. State them here.
4) Is this a right, left or two-tailed test? Sketch a normal curve, mark the critical value and test statistics, and shade the rejection region on the curve.
5) Use your calculator to find the P value. State it here.
6) Do we reject or not reject the null hypothesis? Is there sufficient evidence to conclude that children under the age of 10 consume significantly more sodium than the recommended amount? What kind of implications can you project for the future health of the children and for the economy based on this study?