After an advocacy group found that a chemical plant released industrial soap into the water supply of the city, a study investigates the association between exposure to the industrial soap and skin rash in children. The study is done over a period of 8 years after the the advocacy’s group discovery. The following table shows the descriptive data collected.

A) Find out the incidence of skin rash in the exposed and unexposed.

B) Determine the relative risk for skin rash due to exposure.

C) Interpret your findings

You wish to test the following claim (Ha) at a significance level of α=0.002.

      Ho:μ1=μ2 Ha:μ1<μ2

You believe both populations are normally distributed, but you do not know the standard deviations for either. However, you also have no reason to believe the variances of the two populations are not equal. You obtain a sample of size n1=18 with a mean of M1=59.3 and a standard deviation of SD1=15.2 from the first population. You obtain a sample of size n2=13 with a mean of M2=69.1 and a standard deviation of SD2=5.7 from the second population.

What is the critical value for this test? (Report answer accurate to three decimal places.)
critical value =

What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =

The test statistic is...

• in the critical region
• not in the critical region

This test statistic leads to a decision to...

• reject the null
• accept the null
• fail to reject the null

As such, the final conclusion is that...

• There is sufficient evidence to warrant rejection of the claim that the first population mean is less than the second population mean.
• There is not sufficient evidence to warrant rejection of the claim that the first population mean is less than the second population mean.
• The sample data support the claim that the first population mean is less than the second population mean.
• There is not sufficient sample evidence to support the claim that the first population mean is less than the second population mean.

Please explain and use ti84

The null and alternate hypotheses are: H0 : μd ≤ 0 H1 : μd > 0

The following sample information shows the number of defective units produced on the day shift and the afternoon shift for a sample of four days last month.

Day 1 2 3 4

Day shift 12 12 16 19

Afternoon shift 10 10 12 15

At the 0.010 significance level, can we conclude there are more defects produced on the day shift? Hint: For the calculations, assume the day shift as the first sample.

a. State the decision rule. (Round your answer to 2 decimal places.)

b. Compute the value of the test statistic. (Round your answer to 3 decimal places.)

c. What is the p-value?

d. What is your decision regarding H₀?

A researcher is looking at the correlation between depression and anxiety using a two-tailed test with an alpha level of .05. The researcher finds the following correlation coefficient: r = .22, p = .04. What can the researcher conclude?

a. There is a significant positive relationship between depression and anxiety in this sample.

b. There is no statistically significant relationship between depression and anxiety in this sample.

c. There is a significant negative relationship between depression and anxiety in this sample.

d. Higher levels of depression cause higher rates of anxiety.

A particular fruits weights are normally distributed with a mean of 387 gram and a standard deviation of 13 grams if a fruit is picked at random then 19% of the time its weight will be greater than how many grams give your answer to the nearest gram

1. Consider an LP where you have to determine how much/many of each product to manufacture; there in all, TWO products made from three ingredients. The ingredient usage matrix is as follows. Ingredint1 ingredint2 ingredient3 Product1 1 5 2.5 Product2 4 3 3 Prices of products 1, and 2 are respectively, $65, $55 per unit. Prices of ingredients are respectively, $5, $2 and $4 per unit. You have to formulate an LP to maximize net profit. Product 1 cannot exceed 100 units; ingredient 2 cannot exceed 80 units in consumption.

(a) Define variables (10 points) (You will use these variables for (b)-(d))

(b) Write the objective function. (15)

(c) Write the constraint on the amount of product 1. (10)

(d) Write the constraint ensuring that you do not plan on using more of ingredient 2 than you have available.

Use the provided contingency table and expected frequencies. At alpha equals 0.01​, test the hypothesis that the variables are independent. What is the test statistic?

​Co-browsing refers to the ability to have a contact center agent and customer jointly navigate an application on a real time basis through the web. A study of businesses indicates that 88 of 126 ​co-browsing organizations use​ skills-based routing to match the caller with the right​ agent, whereas 61of 180 ​non-co-browsing organizations use​ skills-based routing to match the caller with the right agent.

a. At the0.01 level of​ significance, is there evidence of a difference between​ co-browsing organizations and​ non-co-browsing organizations in the proportion that use​ skills-based routing to match the caller with the right​ agent? Let π1represent the proportion of​ co-browsing organizations, and let π2 represent the proportion of​ non-co-browsing organizations. What are the null and alternative hypotheses to​ test?

calculate the test statistic

x2stat =

What is the critical value for .01

x2 .01 =

b. The p-value =

b. An earlier​ Z-test for the difference between two proportions in parts​ (a) and​ (b) resulted in a test statistic of ZSTAT=6.19 against critical values of −2.33 and 2.33 with a​ p-value of .000. Compare the results of​ (b) and​ (c) to the results of the​ Z-test.

Using ANOVA Assess attitudes toward same-sex marriages of non-politician republicans and democrats Note:

0 disagree with same-sex marriages and 10 Agree with same-sex marriages

Republicans

6,5,3,7,4

Democrats

8,6,9,8,7

Independent

6,7,5,6,5

The Occupational Safety and Health Administration (OSHA) has identified the gaseous chemical benzene as a possible cancer-causing substance. A federal regulation requires factories to keep the amount of benzene in the air at or below 1 part per million (ppm). OSHA sends an investigator to inspect the air quality at a certain factory. The factory’s manager insists that their air quality is safe. In OSHA’s investigation, they collected 20 random air samples from the factory and found a mean benzene content of 1.4 ppm with a standard deviation of 1.25 ppm.

At a significance level of 0.01, conduct a hypothesis test for the claim, “The air in this factory has a mean benzene content that is less than or equal to 1 ppm.”

1. Select the pair of hypotheses that are appropriate for testing this claim.

2. Select the choice that best describes the nature and direction of a hypothesis test for this claim.

3. Find the standardized test statistic for this hypothesis test. Round your answer to 2 decimal places.

4. Find the P-value for this hypothesis test. Round your answer to 4 decimal places.

5. Using your previous calculations, select the correct decision for this hypothesis test.

6. Consider the following statements related to the claim. Based on the results of your hypothesis test, which of these statements is true? Select the best choice.

) The breaking strength of plastic bags used for packaging produce is normally distributed, with a mean of 17 pounds per square inch and a standard deviation of 9.5 pounds per square inch. What proportion of the bags have a breaking strength of a. less than 14.17 pounds per square inch? _______ b. at least 13.6 pounds per square inch? _______ c. 95% of the breaking strengths will be between what two values symmetrically distributed around the mean? _______ _______ d. less than 13.6 or more than 16.4 _______ e. less than 15 and less than 13.6 f. between 13.6 and 15

Use a 5% significance level for all hypothesis tests (α=.05) unless otherwise noted. Give conclusions as complete sentences. This is considered an ‘open book’ test so you may use the text, StatCrunch, any notes you have, or lecture videos. You should not consult other individuals.

1. A marketing firm was hired by the Acme Company to determine if internet advertising for the company was equally effective in reaching men and women. They sampled 675 men and 703 women and found that 297 of the men and 246 of the women had seen ads for the Acme Company over the previous month.

a) Which test should be performed?

b) State the null and alternative hypotheses.

c) Use StatCrunch to find the test statistic and the p-value.

d) Do you reject or fail to reject the null hypotheses?

e) State the conclusion in a complete sentence.

Correlation

To determine how the number of housing starts is affected by mortgage rates an economist recorded the average mortgage rate and the number of housing starts in a large country for the past 10 years. These data are listed here.

1. What is the dependent and independent variable?

2. Prepare a scatter plot. What is the direction of correlation?

3. What is the equation of the regression line?

4. What is the coefficient of determination (r²) and interpret the meaning of it?

5. Calculate the correlation coefficient (r) and interpret the meaning of it.

6. Predict the number of housing starts if the interest rate is 8.65.

7. Would it be possible to use this regression model to predict the number of housing starts for an interest rate of 2.45? Why?

The following is a list of the first names of 24 fictional students in a statistics class at Cleveland State University. The students are identified by numbering them 01 through 24.
A sample of six students is to be selected by using systematic sampling. The first student to be selected is the one with ID 03. Choose the six students that will be included in the sample.

On the most recent tax cut proposal, a random sample of Democrats and
Republicans in the Congress cast their votes as follows. Are the votes of Democrats and
Republicans independent of each other?
a. State the null and alternative hypotheses.
b. What is the test statistic?
c. Using a .05 significance level, what is the decision rule?
d. Show the test statistic and essential calculations.
e. Interpret you results

Favor    Oppose Abstain

85 78 37 Democrat

118    61 25 Republican