Reference no: EM132277756

Assignment - SAMPLING DISTRIBUTIONS, ESTIMATION and HYPOTHESIS TESTS FOR ONE INDEPENDENT POPULATION

Use the following statistical distribution tables: the Standard Normal Probability Distribution; the t Distribution; the Chi-Square Distribution.

Part 1 - Read Chapter 5 'some Important Sampling Distributions' Sections 5.1, 5.2, 5.3, 5.4, 5.5, 5.6. Review the instructor's prompt 'Zscores' for the sampling distributions and the breeze presentation. Review carefully the applications on the sampling distributions.

Part 2 - Read Chapter 6 'Estimation' Sections 6.1, 6.2, 6.3, 6.4, 6.5, 6.6, 6.7, 6.8; Review the breeze presentation on estimation. Confidence interval on variance is for your review only. Review carefully the applications on estimation techniques and sample size.

Part 3 - Read Chapter 7 'Hypothesis Testing' Sections 7.1, 7.2, 7.5., 7.9 Section 7.7 is for your review only. Review the instructor's prompt '1 SAMPLE TESTS'. Hypothesis testing for variance and standard deviation is for your review only.

Do the following applications after reading the text and reviewing the instructor's prompts and breezes.

These applications entail: the confidence interval on the mean (for large samples-standard normal distribution, for small samples-t distribution), for proportions (standard normal distribution); hypothesis testing on the mean (large samples-standard normal distribution, small samples-t distribution), hypothesis testing on proportions (standard normal distribution); p-value for large samples (standard normal distribution), p-value for proportions (standard normal distribution).

For each application, please perform the three statistical analysis procedures for determining the population parameter: hypothesis testing, confidence interval estimate, p-value (probability value).

1. Escobar et al. (A-3) performed a study to validate a translated version of the Western Ontario and McMaster Universities Osteoarthritis Index (WOMAC) questionnaire used with Spanish - speaking patients with hip or knee osteoarthritis. For the 76 women classified with severe hip pain, WOMAC mean function score (on a scale from 0 to 100 with a higher number indicating less function) was 70.7 with a standard deviation of 14.6. We wish to know if we may conclude that the mean function score for a population of similar women subjects with severe hip pain is less than 75. Test at ∝ = .01.

2. Can we conclude at ∝ = .01 that the mean maximum voluntary ventilation value for apparently healthy college seniors is not 110 liters per minute? A sample of 20 yielded the following values:

132, 33, 91, 108, 67, 169, 54, 203, 190, 133, 96, 30, 187, 21, 63, 166, 84, 110, 157, 138

3. Jaquemin et al. (A-21) conducted a survey among gynecologists-obstetricians in the Flanders region and obtained 295 responses. Of those responding, 90 indicated that they had performed at least one caesarean section on demand every year. Does this study provide sufficient evidence for us to conclude that 25 percent of the gynecologists-obstetricians in the Flanders region perform at least one caesarian section on demand each year? Test at ∝ = .05.

4. Becker et al. (A-23) conducted a study using a sample of 50 ethnic Fijian women. The women completed a self-report questionnaire on dieting and attitudes toward body shape and change. The researchers found that five of the respondents reported at least weekly episodes of binge eating during the previous 6 months. The researcher would like to determine if more than 20 percent of the Fijian women engage in at least weekly episodes of binge eating? Test at ∝ = .05.

5. In an article in the journal Health and Place, Hui and Bell (A-22) found that among 2428 boys ages 7 to 12 years, 461 were overweight or obese. On the basis of this study, can we conclude that more than 15% of the boys ages 7 to 12 in the sampled population are obese or overweight? Let α=.05.

6. A questionnaire was completed by a simple random sample of 250 gynecologists. One of the questions asked was "Have you seen one or more pregnant women during the past year whom you knew to have elevated blood lead levels". 25 gynecologists answered "yes" and 225 answered "no". May we conclude from these data that in the sampled population fewer than 15% have seen during the past year one or more pregnant women with elevated blood lead levels? Let α=.05

PROJECT -

Estimation of the Population Mean of Soft Plaque Deposit (Confidence Interval of the Mean). Estimation of the Population Proportion of Soft Plaque Deposit (Confidence Interval of the Proportion).

This project uses the sample data of the experiment Atassi (A-1), shown here. Assume the variable, soft plaque deposit index, is approximately normally distributed.

In a study of the oral home care practice and reasons for seeking dental care among individuals on renal dialysis, Atassi (A-1) studied 90 subjects on renal dialysis. The oral hygiene status of all subjects was examined using a plaque index with a range of 0 to 3 (0=no soft plaque deposits, 3=an abundance of soft plaque deposits). The following table shows the plaque index scores for all 90 subjects.

1.17; 2.50; 2.00; 2.33; 1.67; 1.33; 1.17; 2.17; 2.17; 1.33; 2.17; 2.00; 2.17; 1.17; 2.50; 2.00; 1.50; 1.50; 1.00; 2.17; 2.17; 1.67; 2.00; 2.00; 1.33; 2.17; 2.83; 1.50; 2.50; 2.33; 0.33; 2.17; 1.83; 2.00; 2.17; 2.00; 1.00; 2.17; 2.17; 1.33; 2.17; 2.50; 0.83; 1.17; 2.17; 2.50; 2.00; 2.50; 0.50; 1.50; 2.00; 2.00; 2.00; 2.00; 1.17; 1.33; 1.67; 2.17; 1.50; 2.00; 1.67; 0.33; 1.50; 2.17; 2.33; 2.33; 1.17; 0.00; 1.50; 2.33; 1.83; 2.67; 0.83; 1.17; 1.50; 2.17; 2.67; 1.50; 2.00; 2.17; 1.33; 2.00; 2.33; 2.00; 2.17; 2.17; 2.00; 2.17; 2.00; 2.17;

This project has two parts.

Part I - Confidence Interval on the Mean

Show the sample data. Describe the purpose for computing a confidence interval for the mean. (What you are setting out to find) Pick a confidence level of your choice.

1. Compute a sample mean.

2. Describe the variable.

3. Describe the confidence level you are taking and its specific meaning.

4. Show the confidence interval formula that you are using.

5. Show the reliability coefficient (critical value).

6. Show all the pertinent computations using the equation editor.

7. Draw a conclusion in the context of the experiment.

Part II - Confidence Interval on the Proportion

Show the sample data. Describe the purpose for computing a confidence interval on the Proportion (What you are setting out to obtain) Pick a confidence level of your choice.

1. Compute a sample proportion of your choice (pick a certain index, count how many times it comes up in the sample, divide this frequency by sample size).

2. Describe the variable.

3. Describe the confidence level you are taking and its specific meaning.

4. Show the confidence interval formula that you are using.

5. Show the reliability coefficient (critical value).

6. Show all the pertinent computations using the equation editor.

7. Draw a conclusion in the context of the experiment.

Attachment:- Assignment Files.rar