Question

An educator claims that the average salary of substitute teachers in school districts in Allegheny County, Pennsylvania, is less than $60 per day. A random sample of ? = 8 school districts is selected, and the daily salaries (in dollars) are shown.

60, 56, 60, 55, 70, 55, 60, 55

Assume the variable is normally distributed. Is there enough evidence to support the

educator’s claim at ? = 0.10? Use R statistical software to calculate.

a) Report the test statistic value and the p-value.

The test statistic value is ________________________.

The p-value is ________________________.

b) What is the conclusion?

c) Use R statistical software and provide the R-code below

Answer 1

Here we want to test that

Ho:- mu = 60 vs Ha:- mu< 60

i.e.

Ho:- the average salary of substitute teachers in school districts in Allegheny County, Pennsylvania, is $60 per day.

Vs

Ha:- the average salary of substitute teachers in school districts in Allegheny County, Pennsylvania, is less than $60 per day.

a)

R output :

> x<-c(60,56,60,55,70,55,60,55)

> t.test(x,alternative = "less",mu = 60,conf.level = 0.90)

One Sample t-test

data: x

t = -0.62598, df = 7, p-value = 0.2756

alternative hypothesis: true mean is less than 60

90 percent confidence interval:

-Inf 61.41789

sample estimates:

mean of x

58.875

The test statistic value :- t = -0.62598,

p-value = 0.2756

b) Decision criteria:we reject Ho if Pvalue < alpha l.o.s.

Here Pvalue = 0.2756 and l.o.s alpha = 0.10

So pvalue = 0.2756 > alpha = 0.10

Therefore we fail to reject Ho.

There is no sufficient evidence to support educator claims that the average salary of substitute teachers in school districts in Allegheny County, Pennsylvania, is less than $60 per day.

So we may conclude that

The average salary of substitute teachers in school districts in Allegheny County, Pennsylvania, is not less than $60 per day.

c)

x<-c(60,56,60,55,70,55,60,55)
t.test(x,alternative = "less",mu = 60,conf.level = 0.90)