Question

The population spends an average of 8 hours per day working, with a standard deviation of 1 hour. A certain researcher believes that Professors work less hours than average and wants to test whether the average hours per day that Profs work is different from the population. This researcher samples 10 professors and asks them how many hours they work per day, leading to the following dataset:

6, 12, 8, 15, 9, 16, 7, 6, 14, 15

Perform the appropriate statistical test and state your conclusions. You will have to select your own alpha value for the test.

Answer 1

Solution:

Here, we have to use one sample z test for the population mean.

The null and alternative hypotheses are given as below:

Null hypothesis: H₀: The average hours per day that Profs Work is not different from the population.

Alternative hypothesis: H_a: The average hours per day that Profs Work is different from the population.

H₀: µ = 8 versus H_a: µ ≠ 8

This is a two tailed test.

The test statistic formula is given as below:

Z = (Xbar - µ)/[σ/sqrt(n)]

From given data, we have

µ = 8

Xbar = 10.8

σ = 1

n = 10

α = 0.05

Critical value = -1.96 and 1.96

(by using z-table or excel)

Z = (10.8 – 8)/[1/sqrt(10)]

Z = 8.8544

P-value = 0.0000

(by using Z-table)

P-value < α = 0.05

So, we reject the null hypothesis

There is sufficient evidence to conclude that the average hours per day that Profs Work is different from the population.