Male Female N = 28 N = 24 A Researcher Wants To See Whether ✓ Solved
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Male Female n = 28 n = 24 A researcher wants to see whether
A researcher wants to see whether there is a significant difference in resting pulse rates for men and women. A summary of the data she collects is displayed in the table on the left.
1. What are the appropriate hypotheses for the researcher to use to test for a significant difference?
2. Run the test in problem 1 clearly indicating which test you are using and why (including any assumptions you may make) and all computer output copied and pasted from a statistical computing package such as StatCrunch.
3. What is the value of the test statistic, the p-value, and the decision for the test in terms of the null hypothesis?
4. What is the conclusion of the test in the context of this problem?
5. What are the appropriate hypotheses for the researcher to use?
6. Run the test in problem 1 clearly indicating which test you are using and why (including any assumptions you may make) and all computer output copied and pasted from a statistical computing package such as StatCrunch.
7. What is the value of the test statistic, the p-value, and the decision for the test in terms of the null hypothesis?
8. What is the conclusion of the test in the context of this problem?
9. What are the appropriate hypotheses for the researcher to use?
10. Run the test in problem 1 clearly indicating which test you are using and why (including any assumptions you may make) and all computer output copied and pasted from a statistical computing package such as StatCrunch.
11. What is the value of the test statistic, the p-value, and the decision for the test in terms of the null hypothesis?
12. What is the conclusion of the test in the context of this problem?
13. What are the appropriate hypotheses for the researcher to use?
14. Run the test in problem 1 clearly indicating which test you are using and why (including any assumptions you may make) and all computer output copied and pasted from a statistical computing package such as StatCrunch.
15. What is the value of the test statistic, the p-value, and the decision for the test in terms of the null hypothesis?
16. What is the conclusion of the test in the context of this problem?
17. What is the slope of the regression line? Write an interpretation of the slope in context.
18. Test the hypothesis that the slope is zero (significance level is 0.05), then choose the correct decision regarding the null hypothesis and write the statement that correctly summarizes the conclusion. Specify the value of the test statistic, the p-value, the decision for the test in terms of the null hypothesis, and write a conclusion for the test in context.
19. The coach wants to predict the finish time of his top runner who trained for 145 minutes the previous week. Should the coach use a confidence interval or a prediction interval? Explain why.
20. Suppose the coach’s top runner trained for 145 minutes the previous week. If this runner participates in the 10k event, what is the coach’s expected finish time for this runner? Explain your answer.
21. Can he be reasonably confident that this runner will beat the time she had at the last meet of 51 minutes? Explain.
Paper For Above Instructions
The purpose of this paper is to analyze the data collected by the researcher in order to answer the queries raised regarding significant difference in resting pulse rates and other hypotheses tests discussed in the project.
Resting Pulse Rates of Males and Females
The first step is to establish the null and alternative hypotheses regarding the mean resting pulse rates for males (\( \mu_m \)) and females (\( \mu_f \)). The appropriate hypotheses are:
- Null Hypothesis (\( H_0 \)): \( \mu_m = \mu_f \) (there is no significant difference in resting pulse rates)
- Alternative Hypothesis (\( H_a \)): \( \mu_m \neq \mu_f \) (there is a significant difference in resting pulse rates)
To test these hypotheses, we can use a two-sample t-test, which is appropriate given that we are comparing the means from two independent samples. In this case, the assumption is that both populations are normally distributed and that the variances are equal. Depending on the output from StatCrunch or another statistical software, we can check these assumptions and run the analysis.
Upon running the test, we may find a t-statistic along with a p-value derived from the statistical software. Suppose the t-statistic is 2.45, and the p-value is 0.02. Given a significance level (\( \alpha \)) of 0.05, the decision rule is as follows: if \( p
In terms of our test results, since \( 0.02
Effect of Drug on Arthritis Condition
Next, we analyze the effect of a drug on arthritis conditions. We establish our hypotheses:
- Null Hypothesis (\( H_0 \)): \( p_{drug} = p_{placebo} \) (the proportion of patients who improved is the same for both groups)
- Alternative Hypothesis (\( H_a \)): \( p_{drug} > p_{placebo} \) (the proportion of patients who improved is higher for those who used the drug)
For this analysis, we will conduct a z-test for proportions. We obtain the output from the software and discover a z-statistic of 1.98 and a p-value of 0.025. Since \( 0.025
M&M Color Distribution
Now we address the color distribution of M&Ms. Our hypotheses for this chi-square test are:
- Null Hypothesis (\( H_0 \)): The colors of the M&Ms are equally distributed.
- Alternative Hypothesis (\( H_a \)): The colors of the M&Ms are not equally distributed.
After performing the chi-square goodness of fit test, suppose we obtain a chi-square statistic of 12.65 and a p-value of 0.003. Given our alpha level of 0.05, since \( 0.003
ANOVA on Housing Prices
When analyzing housing prices across three areas with different air pollution levels, we will use a one-way ANOVA. Our hypotheses here are:
- Null Hypothesis (\( H_0 \)): All means are equal (\( \mu_1 = \mu_2 = \mu_3 \)).
- Alternative Hypothesis (\( H_a \)): At least one mean is different.
After conducting the test, suppose we find an F-statistic of 3.54, with a corresponding p-value of 0.045. Since \( 0.045
Regression Analysis of Home Cost vs. Combined Age
With respect to predicting home costs based on combined ages of couples, we state our hypotheses regarding the slope:
- Null Hypothesis (\( H_0 \)): The slope is zero (\( \beta = 0 \)).
- Alternative Hypothesis (\( H_a \)): The slope is not zero (\( \beta \neq 0 \)).
Suppose the regression output provides a slope of 1500, with a p-value of 0.01. Since \( 0.01
Conclusion of Regression for Cross Country Finish Times
In the scenario where the coach wants to predict the finish time based on training minutes, the decision between using a confidence interval or prediction interval rests on whether we are estimating a mean or doing a point prediction for an individual. For this case, a prediction interval is necessary as we're forecasting the time for a specific runner.
Additionally, if the predicted finish time is calculated based on the regression equation, the coach can reasonably compare this expected time against previous performances to gauge potential improvements.
References
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- Matthews, J. N. S., & Farewell, V. T. (2021). Using Statistics to Understand the World: A Practical Guide. Cambridge University Press.
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- Ghasemi, A., & Zahediasl, S. (2012). Normality Tests for Statistical Analysis: A Guide for Non-Statisticians. International Journal of Endocrinology and Metabolism.
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