Question

Many companies are becoming involved in flextime, in which a worker schedules his or her own work hours or compresses work weeks. A company that was contemplating the installation of a flextime schedule estimated that it needed a minimum mean of 7 hours per day per assembly worker in order to operate effectively. Each of a random sample of 90 of the company's assemblers was asked to submit a tentative flextime schedule. If the mean number of hours per day for Monday was 6.8 hours and the standard deviation was 2.3 hours, do the data provide sufficient evidence to indicate that the mean number of hours worked per day on Mondays, for all of the company's assemblers, will be less than seven hours? Test using α = 0.05. (Round your answers to two decimal places.)

1-2. Null and alternative hypotheses:

H0: μ = 7 versus Ha: μ ≠ 7

H0: μ = 7 versus Ha: μ > 7

H0: μ ≠ 7 versus Ha: μ = 7

H0: μ < 7 versus Ha: μ > 7

H0: μ = 7 versus Ha: μ < 7 3.

Test statistic: z = 4.

Rejection region: If the test is one-tailed, enter NONE for the unused region.

z >

z <

5. Conclusion:

H0 is not rejected. There is insufficient evidence to indicate that the mean number of hours will be less than 7.

H0 is rejected. There is insufficient evidence to indicate that the mean number of hours will be less than 7.

H0 is not rejected. There is sufficient evidence to indicate that the mean number of hours will be less than 7.

H0 is rejected. There is sufficient evidence to indicate that the mean number of hours will be less than 7.

Answer 1

To test against

This is a one tailed test.

Here

sample mean

sample standard deviation

and sample size

Since the sample size is large enough, we can approximate the distribution of sample statistic by normal distribution.

The test statistic can be written as

which under H₀ approximately follows a standard normal distribution.

We reject H₀ at 5% leve of significance if

Now,

The value of the test statistic

and critical value

Since , so we fail to reject H₀ at 5% leve of significance and we can conclude that there is insufficient evidence to indicate that the mean number of hours will be less than 7..

ans-> H0 is not rejected. There is insufficient evidence to indicate that the mean number of hours will be less than 7.