Do teachers find their work rewarding and satisfying? The article presents the results of a survey of 399 primary school teachers and 264 senior teach

pancha3 2020-11-12 Answered
Do teachers find their work rewarding and satisfying? The article presents the results of a survey of 399 primary school teachers and 264 senior teachers. Of the elementary school teachers, 223 said they were very satisfied with their jobs, whereas 127 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.(UsePelementaryPhigh school. Round your answers to four decimal places.)
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Expert Answer

curwyrm
Answered 2020-11-13 Author has 87 answers
Step 1
Let Pelementary denotes the population proportion of all elementary school teachers who are satisfied, and Phigh school denotes the population proportion of all high school teachers who are satisfied. The test assertion is that there is a difference between the proportion of all elementary school teachers who are satisfied and all high school teachers who are satisfied. The hypothesis is,
Null hypothesis:
H0:PelementaryPhigh school=0
Alternative hypothesis:
H1:PelementaryPhigh school0
The sample proportion of all elementary school teatcher who are satisfied is,
P^elementary=x1n1
=223399
=0.5589
The sample proportion of all elementary school teachers who are satisfied is 0.5589.
The sample proportion of all high school teachers who are satisfied is,
P^high school=x1n1
=127264
=0.4811
The sample proportion of all high school teachers who are satisfied is 0.4811.
Step 2
Computation of critical value:
(1α)=0.95
α=0.05
α2=0.025
1α2=0.0975
The critical value of z-distribution can be obtained using the excel formula =NORM.S.INV(0.975)". The critical value is 1.96.
The 95% confidence interval for the difference between the proportion of all elementary school teachers who are satisfied and all high school teachers who are satisfied is, CI=P^elementaryP^high school±zα2P^elementary(1P^elementary)nelementary+P^high school(1P^high school)n(nhigh school)
=(0.55890.4811)±1.960.5589(10.5589)399+0.4811(10.4811)264
=0.0778±0.0775
=(0.07780.0775,0.0778+0.0775)
=(0.0003,0.1553)
Hence, the 95% confidence interval for the difference between the proportion of all elementary school teachers who are satisfied and all high school teachers who are satisfied is (0.0003, 0.1553).
Decision rule:
If the confidence interval does not contains value zero, then reject the null hypothesis.
Conclusion:
The confidence interval does not contain a zero value.
Based on the decision rule, reject the null hypothesis.
Thus, there is difference between the proportion of all elementary school teachers who are satisfied and all high school teachers who are satisfied.
Not exactly what you’re looking for?
Ask My Question

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Relevant Questions

asked 2021-08-03
A simple random sample of 60 items resulted in a sample mean of 80. The population standard deviation is σ=15
a) Compute the 95% confidence interval for the population mean. Round your answers to one decimal place.
b) Assume that the same sample mean was obtained from a sample of 120 items. Provide a 95% confidence interval for the population mean. Round your answers to two decimal places.
c) What is the effect of a larger sample size on the interval estimate?
Larger sample provides a-Select your answer-largersmallerItem 5 margin of error.
asked 2021-08-09

A clinical trial was conducted to test the effectiveness of a drug for treating insomnia in older subjects. Before​ treatment, 13 subjects had a mean wake time of 101.0 min. After​ treatment, the 13 subjects had a mean wake time of 94.6 min and a standard deviation of 24.9 min. Assume that the 13 sample values appear to be from a normally distributed population and construct a 95% confidence interval estimate of the mean wake time for a population with drug treatments. What does the result suggest about the mean wake time of 101.0 min before the​ treatment? Does the drug appear to be​ effective?
Construct the 95% confidence interval estimate of the mean wake time for a population with the treatment.
min<μ<min ​(Round to one decimal place as​ needed.)
What does the result suggest about the mean wake time of 101.0 min before the​ treatment? Does the drug appear to be​ effective?
The confidence interval ▼ does not include| includes the mean wake time of 101.0 min before the​ treatment, so the means before and after the treatment ▼ could be the same |are different. This result suggests that the drug treatment ▼ does not have | has a significant effect.

asked 2021-03-09

In a study of the accuracy of fast food​ drive-through orders, Restaurant A had 298 accurate orders and 51 that were not accurate. a. Construct a 90​% confidence interval estimate of the percentage of orders that are not accurate. b. Compare the results from part​ (a) to this 90​% confidence interval for the percentage of orders that are not accurate at Restaurant​ B: 0.127<p<0.191. What do you​ conclude? a. Construct a 90​% confidence interval. Express the percentages in decimal form. ___

asked 2021-08-12

In a science fair​ project, Emily conducted an experiment in which she tested professional touch therapists to see if they could sense her energy field. She flipped a coin to select either her right hand or her left​ hand, and then she asked the therapists to identify the selected hand by placing their hand just under​ Emily's hand without seeing it and without touching it. Among 358 ​trials, the touch therapists were correct 172 times. Complete parts​ (a) through​ (d).
a) Given that Emily used a coin toss to select either her right hand or her left​ hand, what proportion of correct responses would be expected if the touch therapists made random​ guesses? ​(Type an integer or a decimal. Do not​ round.)
b) Using​ Emily's sample​ results, what is the best point estimate of the​ therapists' success​ rate? ​(Round to three decimal places as​ needed.)
c) Using​ Emily's sample​ results, construct a 90% confidence interval estimate of the proportion of correct responses made by touch therapists.
Round to three decimal places as​ needed - ?<p<?

asked 2022-03-21
Let X1,Xn be iid N(θ, 1). A 95% confidence interval for θ is X±1.96n. Let p denote the probability that an additional independent observation, Xn+1, will fall in this interval. Is p greater than, less than, equal to 0.95? Prove your answer.
asked 2021-08-07
Determine the sample size taken from a normal distribution N(M, 25) to get length of interval of 4 using 90% confidence level for the mean.
asked 2021-08-05

25.623.826.523.924.824.720.92622.227
What Equation to use to construct a 99% lower confidence bound for σ2