Question

In: Statistics and Probability

Do teachers find their work rewarding and satisfying? An article reports the results of a survey...

Do teachers find their work rewarding and satisfying? An article reports the results of a survey of 393 elementary school teachers and 261 high school teachers. Of the elementary school teachers, 221 said they were very satisfied with their jobs, whereas 123 of the high school teachers were very satisfied with their work. Estimate the difference between the proportion of all elementary school teachers who are satisfied and all high school teachers who are satisfied by calculating a 95% CI. (Use pelementary ? phigh school. Round your answers to four decimal places.)

Solutions

Expert Solution

For sample 1, we have that the sample size is N1?=393, the number of favorable cases is X1?=221, so then the sample proportion is ?=X1/N1??=221/393?=0.5623

For sample 2, we have that the sample size is N2?=261, the number of favorable cases is X2?=123, so then the sample proportion is ?=X2/N2 ??=123/261?=0.4713

The value of the pooled proportion is computed as ?=X1?+X2??/N1?+N2? =221+123/?393+261 =0.526

Also, the given significance level is ?=0.05.

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho:p1?=p2?

Ha:p1??p2?

This corresponds to a two-tailed test, for which a z-test for two population proportions needs to be conducted.

(2) Rejection Region

Based on the information provided, the significance level is ?=0.05, and the critical value for a two-tailed test is zc?=1.96.

The rejection region for this two-tailed test is R={z:?z?>1.96}

(3) Test Statistics

The z-statistic is computed as follows:

Z =?

??=0.5623?0.4713?/0.526?(1?0.526)(1/393+1/261)

?=2.284

(4) Decision about the null hypothesis

Since it is observed that ?z?=2.284>zc?=1.96, it is then concluded that the null hypothesis is rejected.

Using the P-value approach: p=0.0224, and since p=0.0224<0.05, it is concluded that the null hypothesis is rejected.

(5) Conclusion

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that population proportion p1? is different than p2?, at the 0.05 significance level.

Confidence Interval

The 95% confidence interval for p1??p2? is: 0.0129<p1??p2?<0.1691 .Since it does not contain zero the confidence interval is significant.


Related Solutions

Do teachers find their work rewarding and satisfying? An article reports the results of a survey...
Do teachers find their work rewarding and satisfying? An article reports the results of a survey of 397 elementary school teachers and 268 high school teachers. Of the elementary school teachers, 225 said they were very satisfied with their jobs, whereas 129 of the high school teachers were very satisfied with their work. Estimate the difference between the proportion of all elementary school teachers who are satisfied and all high school teachers who are satisfied by calculating a 95% CI....
Do teachers find their work rewarding and satisfying? An article reports the results of a survey...
Do teachers find their work rewarding and satisfying? An article reports the results of a survey of 397 elementary school teachers and 268 high school teachers. Of the elementary school teachers, 225 said they were very satisfied with their jobs, whereas 129 of the high school teachers were very satisfied with their work. Estimate the difference between the proportion of all elementary school teachers who are satisfied and all high school teachers who are satisfied by calculating a 95% CI....
Do teachers find their work rewarding and satisfying? An article reports the results of a survey...
Do teachers find their work rewarding and satisfying? An article reports the results of a survey of 397 elementary school teachers and 261 high school teachers. Of the elementary school teachers, 223 said they were very satisfied with their jobs, whereas 121 of the high school teachers were very satisfied with their work. Estimate the difference between the proportion of all elementary school teachers who are satisfied and all high school teachers who are satisfied by calculating a 95% CI....
Do teachers find their work rewarding and satisfying? An article reports the results of a survey...
Do teachers find their work rewarding and satisfying? An article reports the results of a survey of 399 elementary school teachers and 261 high school teachers. Of the elementary school teachers, 227 said they were very satisfied with their jobs, whereas 128 of the high school teachers were very satisfied with their work. Estimate the difference between the proportion of all elementary school teachers who are satisfied and all high school teachers who are satisfied by calculating a 95% CI....
Do teachers find their work rewarding and satisfying? An article in Psychological Reports reported the results...
Do teachers find their work rewarding and satisfying? An article in Psychological Reports reported the results of a survey of a random sample of 395 elementary teachers and 266 high school teachers. Of the elementary school teachers, 224 said that they were very satisfied with their jobs, whereas 166 of the high school teachers were very satisfied with their work. a. Based on this data, is it reasonable to conclude that the proportion of very satisfied teachers is different for...
Find an article that discusses the results of a survey poll. Discuss and critique their methodology, results, and discussion.
  Find an article that discusses the results of a survey poll. Discuss and critique their methodology, results, and discussion. For example, was an appropriate sampling method used to support their results? Was a confidence interval provided? What does the confidence interval mean? How confident do you feel with their results based on their methodology?
find a research article that reports the results using confidence intervals or coefficient values. Discuss the...
find a research article that reports the results using confidence intervals or coefficient values. Discuss the importance of the confidence intervals or coefficient values for proving or disproving the hypotheses. Attach the pdf of the article to your discussion pos
An October 25, 2012 article in the New England Journal of Medicine reports the results of...
An October 25, 2012 article in the New England Journal of Medicine reports the results of a study examining aspirin and survival among patients with colorectal cancer. The following pieces of text are taken directly from the article abstract: (my edits are in italics) “METHODS We obtained data on 964 patients with rectal or colon cancer from the Nurses’ Health Study and the Health Professionals Follow-up Study, including data on aspirin use after diagnosis and the presence or absence of...
An article presents results of a survey of adults with diabetes. The average body mass index...
An article presents results of a survey of adults with diabetes. The average body mass index (BMI) in a sample of 15 men was 30.4, with a standard deviation of 0.6. The average BMI in a sample of 19 women was 31.1 with a standard deviation of 0.2. Assuming BMI is normally distributed, find a 95% confidence bound for the difference in mean BMI between men and women with diabetes. Be sure to interpret the interval in context.
An article summarized results from a national survey of 2302 Americans age 8 to 18. The...
An article summarized results from a national survey of 2302 Americans age 8 to 18. The sample was selected in a way that was expected to result in a sample representative of Americans in this age group. a) Of those surveyed, 1126 reported owning a cell phone. Use this information to construct a 90% confidence interval estimate of the proportion of all Americans age 8 to 18 who own a cell phone. (Round your answers to three decimal places.) (___________...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT