Question

In: Statistics and Probability

A random sample of 1515 teachers from Winnipeg produced an average annual salary of $35,270 with...

A random sample of 1515 teachers from Winnipeg produced an average annual salary of $35,270 with a standard deviation of $3,256. A random sample of 2020 teachers from Brandon produced an average salary of $32,268 with a standard deviation of $2,532

a) (7 points) Using critical value approach test at 2%significance level whether the true mean annual salaries for all teachers in both cities are different? State the assumption(s) required for the test.

b) (3 points) Construct a 98% confidence interval for the difference between true mean annual salaries and test the hypothesis in (a).

Solutions

Expert Solution

Please upvote my answer if you find it helpful. Thanking you.


Related Solutions

uppose the following data were collected from a sample of 1515 CEOs relating annual salary to...
uppose the following data were collected from a sample of 1515 CEOs relating annual salary to years of experience and the economic sector their company belongs to. Use statistical software to find the following regression equation: SALARYi=b0+b1EXPERIENCEi+b2SERVICEi+b3INDUSTRIALi+eiSALARYi=b0+b1EXPERIENCEi+b2SERVICEi+b3INDUSTRIALi+ei. Is there enough evidence to support the claim that on average, CEOs in the service sector have lower salaries than CEOs in the financial sector at the 0.050.05 level of significance? If yes, write the regression equation in the spaces provided with answers...
Suppose the following data were collected from a sample of 1515 CEOs relating annual salary to...
Suppose the following data were collected from a sample of 1515 CEOs relating annual salary to years of experience and the economic sector their company belongs to. Use statistical software to find the following regression equation: SALARYi=b0+b1EXPERIENCEi+b2SERVICEi+b3INDUSTRIALi+eiSALARYi=b0+b1EXPERIENCEi+b2SERVICEi+b3INDUSTRIALi+ei. Is there enough evidence to support the claim that on average, CEOs in the service sector have lower salaries than CEOs in the financial sector at the 0.050.05 level of significance? If yes, write the regression equation in the spaces provided with answers...
2.In a sample of 15 random people from a small town, the average salary is $25,778...
2.In a sample of 15 random people from a small town, the average salary is $25,778 with a standard deviation of $11,540. Use a 5% significance level to test the claim that mean salary in this town is less than $30,000
A random sample of 23 chemists from Washington state shows an average salary of $46066 with...
A random sample of 23 chemists from Washington state shows an average salary of $46066 with a standard deviation of $772. A random sample of 21 chemists from Florida state shows an average salary of $40860 with a standard deviation of $772. A chemist that has worked in both states believes that chemists in Washington make a different amount than chemists in Florida. At αα=0.05 is this chemist correct? Let Washington be sample 1 and Florida be sample 2. The...
A random sample of 15 chemists from Washington state shows an average salary of $46613 with...
A random sample of 15 chemists from Washington state shows an average salary of $46613 with a standard deviation of $775. A random sample of 24 chemists from Florida state shows an average salary of $47757 with a standard deviation of $872. A chemist that has worked in both states believes that chemists in Washington make a different amount than chemists in Florida. At α α =0.01 is this chemist correct? Let Washington be sample 1 and Florida be sample...
In a current study, a random sample of 20 teachers from Texas and an independent random...
In a current study, a random sample of 20 teachers from Texas and an independent random sample of 20 teachers from Indiana have been asked to report their annual income. The data obtained are as follows: Annual income in dollars Texas 36428, 47516, 30452, 33084, 49005, 27069, 30650, 37243, 32531, 37394, 48089, 38013, 44729, 25913, 41093 41199, 32775, 33773, 36110, 43329 Indiana 49281, 46645, 48434, 51386, 39959, 34413, 49065, 35413, 33934, 40901, 35575, 35369, 41076, 41661, 42299 33578, 42152, 39115,...
The annual salary of teachers in a certain state has a mean of μ = $...
The annual salary of teachers in a certain state has a mean of μ = $ 54,000 and standard deviation of σ = $ 5,000 . What is the probability that the mean annual salary of a random sample of 5 teachers from this state is more than $60,000?
A random sample of professional wrestlers was obtained, and the annual salary (in dollars) for each...
A random sample of professional wrestlers was obtained, and the annual salary (in dollars) for each was recorded. The summary statistics were x = 45,500 and n = 17. Assume the distribution of annual salary is normal with o = 8,500. (a) Find a 90% confidence interval for the true mean annual salary for all professional wrestlers (in dollars). (Round your answers to four decimal places.) (______________ , ______________) kg
A random sample of 165 accountants and auditors had an average salary of $70,130 and a...
A random sample of 165 accountants and auditors had an average salary of $70,130 and a standard deviation in salary of $14,400. Another random sample of 182 loan officers had an average salary of $67,960 and a standard deviation in salary of $13,600. Construct a 98% confidence interval for the difference in mean salary between the two professions.
In a random sample of 120 car batteries produced by a special method, the sample average...
In a random sample of 120 car batteries produced by a special method, the sample average lifetime was 135 hours and the sample standard deviation was 12 hours. An engineer claims that the mean lifetime is between 132.452 and 137.548 hours. Assume data is normally distributed. (a) What level of confidence can this statement be made with? (b) Create a confidence interval for the population variance and explain how you did it. State your conclusion.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT