Question

An employee group for a retailer claims that the mean time spent by employees on a personal phone call is less than 10 minutes per day. A random sample of 25 employees is taken and showed a mean of 9.2 minutes and a standard deviation of 2 minutes. Test the claim with a 5% significance level the time is less than 10 minutes.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 10
Alternative Hypothesis, Ha: μ < 10

Rejection Region
This is left tailed test, for α = 0.05 and df = 24
Critical value of t is -1.711.
Hence reject H0 if t < -1.711

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (9.2 - 10)/(2/sqrt(25))
t = -2

P-value Approach
P-value = 0.0285
As P-value < 0.05, reject the null hypothesis.

There is sufficient evidence to conclude that less than 10 mins are spent