# Statistical analysis: Hypothesis Testing

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Use the traditional method of hypothesis testing unless otherwise specified

1. A traffic safety expert report indicated that 21-24 years age group, 31.58% of traffic fatalities were victims who had used a seat belt. Victims who were not wearing a seat belt accounted for 59.83% of the deaths, and the status of the rest was unknown. A study of 120 traffic fatalities in a particular region showed that for this age group, 35 of the victims had used a seat belt, 78 had not, and the status of the rest was unknown. At = 0.05 is there sufficient evidence that the proportions differ from those in the report?

3. Tire Labeling The federal government has proposed labeling tires by fuel efficiency to save fuel and cut emissions. A survey was taken to see who would use these labels. At = 0.10, is the gender of the individual related to whether or not a person would use these labels? The data from a sample are shown here. Gender: Men: Yes -114 No-30 Undecided-6)Women: Yes-136 No-16 Undecided-8

5. Pension Investments A survey was taken on how a lump-sum pension would be invested by 45-year-olds and 65-year-olds. The data are shown here. At = 0.05, is there a relationship between the age of the investor and the way the money would be invested? Age 45: Large Company stocks funds 20, Small company stocks funds 10, International stock funds 10, CDs or money market funds 15, Bond 45. Age 65: Large stock funds 42, small company stock funds 24, International stocks funds 24, CDs or money market funds 6, Bonds 24

7. Employment of High School Females A guidance counselor wishes to determine if the proportions of high school girls in his school district who have jobs are equal to the national average of 36%. He surveys 80 female students, ages 16 through 18, to determine if they work. The results are shown. At = 0.01, test the claim that the proportions of girls who work are equal. Use the P-value method. 16 year olds: work 45, don't work 35 total 80)17 years old: work 31, don't work 49 total 80) 18 year olds: work 38, don't work 42 total 80

9. Health Insurance coverage based on the following data showing the numbers of people (in thousands) with and without health insurance ,can it be concluded at the = 0.01 level of significance that the proportion with or without health insurance is related to the state chosen? With insurance- Arkansas 52, Montana 793, North Dakota 553,Wyoming447. Without insurance - Arkansas 123, Montana 146,North Dakota 61,Wyoming 70

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The hypothesis testing and statistical analysis are examined.

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1.

Null hypothesis: proportions are same from those in the report.

Alternative hypothesis: proportions differ from those in the report.

This is a chi square test.

The degree of freedom is 3-1=2.

The critical chi square value is 5.991

Expected value:

120*31.58%=37.896

120*59.83%=71.796

120-37.896-71.796=10.308

Test value=(35-37.896)^2/37.896+(78-71.796)^2/71.796+(120-78-35-10.308)^2/10.308=1.819

Since 1.819<5.991, we could not reject null hypothesis.

Therefore, there is no sufficient evidence that the proportions differ from those in the report.

3.

Null hypothesis: there is no association.

Alternative hypothesis: there is association.

This is a chi square test.

The degree of freedom is (3-1)*(2-1)=2.

At 0.10 significance level, the critical chi square value is 4.605

Men Women total

yes 114 136 250

no 30 16 46

undecided 6 8 14

total 150 160 310

Expected value: men-yes: 150*250/310=121.0; women-yes: 160*250/310=129.0

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