# General Statistics Questions

### Question Description

I’m working on a statistics test / quiz prep and need guidance to help me study.

*(Assume all distributions are normally distributed.)* 1a) State H0 and Ha

b) Find the critical value, show work

c) Find the appropriate test statistic, show correct substitution of values in formulas. d) Do a P – value test

e) Make a decision to reject or fail to reject the null hypothesis and interpret the results. The hypothesized mean body temperature of a human being is accepted to be equal to 98.6ºF. Researchers at the University of Maryland used the latest equipment and employed rigorous

methodology to determine the average human body temperature from a sample of 148 healthy men and women aged 18 through 40 years. Taking temperature readings from these 148 peoplespaced out at various times throughout the day, they found that the average human bodytemperature is closer to 98.2 °F and used a previously known population standard deviation of 1.62ºF. Test this at α = .05.

2a) State H0 and Ha

b) Find the critical value, show work

c) Find the appropriate test statistic, show correct substitution of values in formulas. d) Do a P – value test

e) Make a decision to reject or fail to reject the null hypothesis and interpret the results. Population 1= male math scores Population 2 = female math scores The mean score on a math assessment test for 35 randomly selected male high school students was 27. Assume the population standard deviation is 4.2. The mean score on the same test for 32 randomly selected female students was 25.5 with a population standard deviation of 3.3. Can you support the claim that mean male math scores are higher than the mean female scores? Test at α = .05.

3a) State H0 and Ha

b) Find the critical value, show work

c) Find the appropriate test statistic, show correct substitution of values in formulas. d) Do a Rejection Region Test

e) Make a decision to reject or fail to reject the null hypothesis and interpret the results. According to the CDC, (Center for Disease Control), as of April 11, at most 21% of U.S. adults have been fully vaccinated. MN Dept of Health has felt the state’s vaccination rate is significantly hire. A random sample of 500 Minnesotans was taken recently and 120 were found to be fully vaccinated. Test the appropriate hypothesis using α = .01. This is a one sample test.

4a) State H0 and Ha

b) Find the critical value, show work

c) Find the appropriate test statistic, show correct substitution of values in formulas. d) Do a Rejection Region Test

e) Make a decision to reject or fail to reject the null hypothesis and interpret the results. A high school district states that their mean ACT scores for the previous year was 21. A school counselor randomly samples 15 students and found the mean sample score was 24 with a sample standard deviation of 5.5. Is there a significant difference? Test at α = .01

5a) State H0 and Ha

b) Find the critical value, show work

c) Find the appropriate test statistic, show correct substitution of values in formulas. d) Do a P – value test

e) Make a decision to reject or fail to reject the null hypothesis and interpret the results. A health research group notices that New Mexico has the highest vaccination rate. They randomly sample 400 adults from New Mexico and find 116 adults have been fully vaccinated. The group also notices that Georgia has the lowest rate and they randomly sample 440 adults and find 66 have been fully vaccinated. Is there a significant difference in the vaccination rate of these 2 states? Test at α = .01. *Round *p* to 2 decimal places.

Pop 1 = New Mexico Pop 2 = Georgia

6a) State H0 and Ha

b) Find the critical value, show work

c) Find the appropriate test statistic, show correct substitution of values in formulas. d) Do a Rejection Region Test

e) Make a decision to reject or fail to reject the null hypothesis and interpret the results. A Minnesota politician states the mean income level is less in St Paul vs Minneapolis. A demographer at the Univ of Minn tests this data and the results are displayed below. Test at α = .05. Assume population variances equal. (Hint on this one: section 8.2) St Paul: 1 11 *Mean** x** s n *: 58500 4100 27 = = =

Minneapolis: 2 22 *Mean** x** s n *: 60400 3700 25 = = =

7a) State H0 and Ha

b) Find the critical value, show work

c) Find the appropriate test statistic, show correct substitution of values in formulas. d) Do a P-Value Test

e) Make a decision to reject or fail to reject the null hypothesis and interpret the results. A physical fitness instructor claims that if users follow his exercise regimen and prescribed diet, they will lose a considerable amount of weight in one month. The weights of a random sample of users before and after one month are shown below. Test at α = .05.

Subject | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |

Before | 205 | 210 | 245 | 256 | 180 | 212 | 215 | 220 | 225 | 233 |

After | 201 | 208 | 241 | 250 | 180 | 210 | 206 | 217 | 217 | 233 |

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