2. (10 pts) The starting salary for 8 randomly selected high school teachers in

Question

2. (10 pts) The starting salary for 8 randomly selected high school teachers in the Bay Area are listed below. 39,775 44,221 44,318 45,697 47,023 48,847 53,851 55,705 Obtain a point estimate for the mean and standard deviation of the starting salary for a high school teacher in the Bay Area. (Ok to use technology) Verify that the assumptions are met for constructing a valid confidence interval for ? . Be specific and use complete sentences. A normal probability plot can be constructed on StatCrunch or Excel. Use the upper and lower fences to determine outliers (full box-plot is not needed). Construct a 95% confidence interval for ?. lecture notes and interpret in a complete sentence. Nationwide, the starting salary for a high school teacher is $30,377. What conclusion can you draw using the confidence interval found in c)? Why might this be? a) b) 2 c) Show all steps as shown in 5 2 d)

Explanation / Answer

A)
mean= 47,429.6250 AVERAGE
sd= 5,257.14 STDEV

B)

From the normal probability plot observed at the point form an S-shape. This indicates that the assumption of normality is followed.

C)
alpha= 5%

T(a/2,n-1)
t(0.05/2,8-1)
2.365

CI = mean +-t(a/2,n-1)*(sd/sqrt(n))
lower = 47429.625-2.365*(5257.14400839467/sqrt(8))= 43033.84
upper = 47429.625 + 2.365*(5257.14400839467/sqrt(8))= 51825.41

I am 95% confidence that estimated population mean salary for high school teachers in the Bay area lie in the interval (43033.84, 51825.41)

D)

Since the above confidence interval does not contain 30377, I reject the null hypothesis. Hence I can conclude that nationwide, the starting salary for high school teacher is not 30377.

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