Question

In: Statistics and Probability

The Digest of Educational Statistics reported that the mean salary for teachers in 2012 was $56,410....

The Digest of Educational Statistics reported that the mean salary for teachers in 2012 was $56,410. Assume that this information is based on a sample of 101 teachers and the sample standard deviation was $15,000.   

  1. Does this situation meet the conditions for the t-interval of the population mean?

  1. What is the df (degrees of freedom) for this situation?   

  1. What is the critical t-value you would use for a 90% confidence interval? (table)  

  1. What is the calculated margin of error?   

  1. What is the 90% confidence interval?

Solutions

Expert Solution

Solution :

Given that,

Yes.using the  t-interval

Point estimate = sample mean = = 56410

sample standard deviation = s = 15000

sample size = n = 101

Degrees of freedom = df = n - 1 = 101 -1 =100

At 90% confidence level

= 1-0.90% =1-0.9 =0.10

/2 =0.10/ 2= 0.05

t/2,df = t0.05,100 = 1.66

Critical value = t /2,df = 1.66

Margin of error = E = t/2,df * (s /n)

= 1.66 * ( 15000/ 101)

Margin of error = E =2477.99

The 90% confidence interval estimate of the population mean is,

- E < <  + E

56410 -2477.99 < < 56410 +2477.99

53932.01 < < 58887.99.

(53932.01,58887.99.)

orchestra answered 1 year ago
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