Problem: Three different techniques were used to lower the blood pressure of individuals diagnosed with high blood pressure. The subjects are randomly assigned to three groups and after a period of 4 weeks the reduction in each person’s blood is recorded. The results are as follows:

Analyze the data using one way ANOVA and test your claim at \[\alpha =0.05\] . Give a short description for each step of your analysis.

1. State the null and alternative hypotheses.
2. Construct the error bar for this distribution and comment on the graphs.

© Show your tables generated and comment on the Descriptives and give your interpretation of the ANOVA table.

(d) State your null and alternative hypotheses for variance and interpret your Levene’s test of homogeneity for variances.

(e) Use Scheffé Test and Tukey’s test to determine any differences and comment on the results.

Q 2 ) If the 95% confidence interval for the mean weight of infants born to mothers who smoke is found to be 5.3 pounds to 6.5 pounds using the formula \[\overset{\_}{\mathop{x}}\,\pm {{z}_{1-\frac{\alpha }{2}}}\frac{\sigma }{\sqrt{n}}\] .

1. What is the value of the sample mean used to calculate the confidence interval?
2. What is margin of error of the confidence interval?
3. What is the standard error of the estimate?
4. Calculate the 99% confidence interval for μ.
5. The sample mean is significantly different from 7.2 pounds at α = 0.05. Is the difference significant at α = 0.01?

Q 3 ) A variable has a standard deviation of 40 mg/dL. We want to test a mean difference in two groups with α = 0.05 (two sided) and power 84%.

1. How many observations are needed to detect a difference of 10 mg/dL?
2. Suppose we can recruit only 230 subjects into group 1. How many individuals do we need in group 2?

Q 4 ) Data for suspended particulate matter in air particles at two sites are given below in \[\mu gms/{{m}^{3}}\] .

Site 1: 68 22 36 32 42 24 28 38 35 37

Site 2: 36 38 39 40 36 35 34 33 32 37

Complete the table below:

1. Calculate the standard error of the mean difference without assuming equal variances.
2. Create back to back stem plots for the data.
3. Calculate a 95% confidence interval for \[{{\mu }_{1}}-{{\mu }_{2}}\] , again without assuming equal variance. Use the conservative degrees of freedom to help calculate the confidence interval.
4. State the null and alternative hypothesis and determine the two-sided p-value for testing: \[{{H}_{0}}:{{\mu }_{1}}={{\mu }_{2}}\] .
5. Compare you results against a significant level of 0.05 and interpret your results.

Q 5 ) The data below shows the number of items of a new product sold over a period of 15 months at a certain store.

(a) Draw the scatter plot for the data.

(b) Find the equation of the regression line and plot using SPSS.

© Describe how the line fits the data.

(d) Using the transform command, create a new variable for x by generating log x .

(e) Using the log x values as the independent variable, find the equation of the regression line and plot the regression line using SPSS.

(f) Compare the two plots (one with x variable and the other with log x) and give your interpretation as to which one fits the data better.

(g) From your SPSS tables, compute r and \[{{r}^{2}}\] for both sets of data. Discuss give your interpretation of these values.

(h) Give your opinion as to which line would be a better predictor for the data and why.

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