Question

Letter B

3. Imagine you work for an institutional research department at Randy State University. Five years ago, you conducted a survey of all University staff and determined their average ratings workplace satisfaction was 6.3 (out of a possible 10). A lot has changed at Randy State over the past few years, the University has grown substantially allowing for raises to be given to all employees. You are interested in seeing if these changes have led to an increase in workplace satisfaction so you conduct a new survey on a sample of 20 employees and find that the average satisfaction rating is 7.4 with a standard deviation of 2.2

Answer 1

  $H_o:\mu= 6.3\\H_a:\mu>6.3$

Values are given as

mu = 6.3

n = 20

x = 7.4

s= 2.2

df = (n-1)=(20-1)=19

using this  formula when sample size is less than 30

$t= (x-\mu) / (s/\sqrt{n})$

put the values

$t= (7.4-6.3) / (2.2/\sqrt{20})$

= 1.1 / 0.4919

t= 2.2362

using (df=19) , (alpha = 0.01) in t table we get the p value

p= 0.0188

0.0188 >0.01

p value is greater than alpha so , we failed to reject the null hypotheses