1.

Rhino viruses typically cause common colds. In a test of the effectiveness of echinacea, 32 of rhe 46 subjects treared with echinacea developed rhinovirus infections. In a placebo group, 44 of the 71 subjects developed rhinovirus infections. Using a 0.06 significance level, test the claim that echinacea has an effect on rhinovirus infections.

a) Determine the critical value.

b) Determine the test statistic.

c) Decide whether or not we reject or fail to reject the null hypothesis.

d) State whether or not there was sufficient evidence to support the claim.

e) Construct the confidence interval about the difference between the two proportions.

Write the confidence interval as (LowerValue, HigherValue)

critical value =9 decimals

test statistic =(12 decimals)

[Select Decision]

We reject the null hypothesis

We fail to reject the null hypothesis

We accept the alternate hypothesis

[Select Conclusion]

With a 94% level of confidence, we can say echinacea has an effect on rhinovirus infections.

There is not enough evidence to suggest echinacea has an effect on rhinovirus infections.

Confidence Interval about p₁-p₂:(12 decimals,11 decimals)

2.

The herb ginkgo biloba is commonly used as a treatment to prevent dementia. In a study of the effectiveness of this treatment, 846 elderly subjects were given ginkgo and 823 elderly subjects were given a placebo. Among those in the ginkgo treatment group, 85 later developed dementia, and among those in the placebo group, 107 later developed dementia. We want to use a 0.02 significance level to test the claim that ginkgo is effective in preventing dementia.

a) Determine the critical value.

b) Determine the test statistic.

c) Decide whether or not we reject or fail to reject the null hypothesis.

d) State whether or not there was sufficient evidence to support the claim.

e) Construct the confidence interval about the difference between the two proportions.

Write the confidence interval as (LowerValue, HigherValue)

critical value =(9 decimals)

test statistic =(11 decimals)

[Select Decision]

We reject the null hypothesis

We fail to reject the null hypothesis

We accept the alternate hypothesis

[Select Conclusion]

With a 98% level of confidence, we can say ginkgo is effective in preventing dementia.

There is not enough evidence to suggest ginkgo is effective in preventing dementia.

Confidence Interval about p₁-p₂:(13 decimals,13 decimals)

3.

People spend around $5 billion annually for the purchase of magnets used to treat a wide variety of pains. Researchers conducted a study to determine whether magnets are effective in creating back pain. Pain was measured using the visual analog scale (VAS scaled from 0 to 1 where 1 represents 100% pain reduction and 0 represents no pain reduction), and the results given below are among the results obtained in the study--the larger the VAS, the more effective in pain reduction. Use a 0.05 significance level to test the claim that those treated with magnets have a greater mean reduction in pain than those given a sham treatment (similar to a placebo).

Reduction in Pain Level After Magnet Treatment: n₁= 44, x₁= 0.26, s₁= 0.029

Reduction in Pain Level After Magnet Treatment: n₂= 38, x₂= 0.24, s₂= 0.027

critical value =(9 decimals)

test statistic =(11 decimals)

[Select Decision]

We reject the null hypothesis

We fail to reject the null hypothesis

We accept the alternate hypothesis

[Select Conclusion]

With a 98% level of confidence, we can say those treated with magnets have a greater mean reduction in pain than those given a sham treatment.

There is not enough evidence to suggest those treated with magnets have a greater mean reduction in pain than those given a sham treatment.

4.

In a study of proctored and non proctored tests in an online Intermediate Algebra course, researchers obtained the data for test results given below. With a 98% level of confidence determine if it seems to make a difference whether or not the online tests are proctored.

Data for the proctored group: {57.8, 51.7, 79, 93.7, 76.8, 84.7, 89.8, 90.8, 95.8, 44.9, 76.4, 95.2, 87.4}

Data for the non-proctored group: {89.9, 77.9, 82.3, 68.5, 80.6, 91.3, 83.2, 71.6, 70.7, 81.5}

critical value =(9 decimals)

test statistic =(11 decimals)

[Select Decision]

We reject the null hypothesis

We fail to reject the null hypothesis

We accept the alternate hypothesis

[Select Conclusion]

With a 98% level of confidence, we can say it seems to make a difference whether or not the online tests are proctored.

There is not enough evidence to suggest it seems to make a difference whether or not the online tests are proctored.

5.

A study was conducted to see if there is a relationship between CEO pay and average full time employee pay. Data was collected from the base salaries of 9 CEO's and the mean average salaries of full time employes of the companies of theses CEOs. Use a 0.05 level of significance and the data below to determine the critical value of Pearson Correlation Coeficient, the test statistic, and determine whether or not there seems to be a correlation between the two. If so, what type of correlation exists?

CEO Salary$522000$1973000$2423000$2892000$973000$2352000$1893000$558000$697000Mean employee salary$49700$45400$45100$42900$48800$43300$47000$48900$50800

critical value =(12 decimals)

test statistic =(12 decimals)

[Select Conclusion]

With a 0.05 level of significance, we can say there is a positive correlation between these two values

With a 0.05 level of significance, we can say there is a negative correlation between these two values

There is not enough evidence to suggest there is a correlation between these two values

6.

A study by a prominent researcher tried to determine whether or not there is a correlation between per household gun ownership and the number of deaths caused by guns (per capita). The information shown below was gathered from 12 cities in the United States over the course of one year. Determine the equation of the regression line that best fits this data.

(write your answer as = mx + b).

Then, predict the number of firearm deaths in a city that has 309.2 guns per 1000 households.

Gun ownership

(per 1000 households)231.8640.6293.8414166.4458.4627.4260.1432.2340586.9220Gun deaths

(per 100,000 people)9.217.710.513.27.714.117.59.913.411.516.78.8

=(14 decimals+11 decimals)

y(309.2) =

7.

A study of smokers determined that there is a correlation between the number of cigarettes smoked per day and the age of death. The data for this study is shown below.Determine the equation of the regression line that best fits this data.

(write your answer as = mx + b).

Then, predict the age to which one is expected to live if s/he smokes on average 22.5 cigarettes per day.

Avg num cigarettes

smoked/day2717.836.318.515.525.622.937.52228.336.532.318.913.827.2Age of death68.176.16675.971.769.671.765.867.969.561.264.469.473.266.9

=(12 decimals+10 decimals)

y(22.5) =

8.

The Thing Factory is a factory that manufactures all kinds of things. They place these things in a batch with an expected proportion amount for each thing. During an audit the auditor compared the observed number of things in a batch with the expected number of things for the batch. With a 0.01 level of significance, determine whether or not the observed batch is a good fit with what is expected.

Determine the critical value for the²Goodness of Fit Test.

Determine the test statistic for the²Goodness of Fit Test.

Verify whether or not observed batch is a good fit with what is expected.

CategoryObserved NumExpected Numcumsiecoms4942dingbats7081gizmoes4046hoozy-whatzies8171

²critical value =(8 decimals)

²test statistic =(11 decimals)

[Select Decision]

There seems to be a good fit with what is expected

With a 0.01 level of significance, there does not seem to be a good fit with what is expected

9.

The table below shows the results (in percent) for each candidate running for the same seat in the state senate. The observed values were the actual final tally for each candidate after all the votes were counted. With a 0.01 level of significance, determine whether or not the observed results are a good fit with the expected percent results.

Determine the critical value for the²Goodness of Fit Test.

Determine the test statistic for the²Goodness of Fit Test.

Verify whether or not observed batch is a good fit with what is expected.

CategoryExpected PercentObserved NumSwirvithan L'Goodling-Splatt17.2566666667%33Sequester Grundelplith M.D.9.28666666667%28Blyrone Blashinton13.4766666667%48Cartoons Plural18.1166666667%40Cosgrove Shumway14.4766666667%38Fozzy Whittaker27.3866666667%62

²critical value =(8 decimals)

²test statistic =(10 decimals)

[Select Decision]

There seems to be a good fit with what is expected

With a 0.01 level of significance, there does not seem to be a good fit with what is expected