Question

A random sample of 25 employees for the retailer showed a sample mean of 15.1 minutes and a standard deviation of 3 minutes. Assume that the time spent by employees on personal phone calls is normally distributed. Let μ denote the mean time spent by employees spent on personal phone calls.

(a) An employee group for a national retailer claims that the mean time spent by employees on personal phone calls is more than 20 minutes per day. Specify the correct null and alternative hypotheses to investigate the employee group’s claim.

(b) Find the value of the standardized test statistic.

(c) Find the rejection region at α = .05 and state your conclusion in the context of the problem.

(d) State the Type I error based on the context of the problem

Answer 1

n=25,  = 20,   = 0.05

= 15.1 , s= 3

a)

null and alternative hypothesis is

Ho:     20

H1:   > 20

b)

formula for test statistics is

t = -8.167

test statistics= -8.167

c)

calculate t critical value for right tailed test with df= n-1 = 25-1 = 24

using t table we get critical value as follows

Critical value= 1.711

rejection region is as follows,

decision rule is

Reject Ho if ( t ) > ( 1.711)

here, ( t= -8.167 ) < ( 1.711 )

Hence, we can say,

Null hypothesis is NOT rejected.

There is NOT sufficient evidence to support th claim that the mean time spent by employees on personal phone calls is more than 20 minutes per day.

d)

type I error occurs when we reject the true null hypothesis.

In these context type I error occurs when we conclude that the mean time spent by employees on personal phone calls is more than 20 minutes per day.

but in fact  mean time spent by employees on personal phone calls is less than or equal to 20 minutes per day,