Question

In order to gain information on the required stocking levels of hospital resources, a study was conducted into the usage of latex gloves by hospital employees. Previous orders worked on the belief that the average number of gloves used per employee per week for all employees in the hospital was greater than 23. The resource manager tests this by sampling n = 35 hospital employees and found that number of gloves used by the sampled workers were summarized by an average of 20.74 and a standard deviation of s = 11. The hypotheses being tested are: H 0: μ = 23 H a: μ > 23.

An estimate of the population mean is .

The standard error is .

The distribution is (examples: normal / t12 / chisquare4 / F5,6).

The test statistic has value TS= .

Testing at significance level α = 0.01, the rejection region is:___________ (less/greater) than__________ (2 dec places).

Since the test statistic (is in/is not in) the rejection region, there (is evidence/is no evidence) to reject the null hypothesis, H 0.

There (is sufficient/is insufficient) evidence to suggest that the average number of gloves used by all employess per week, μ, is greater than 23 .

Were any assumptions required in order for this inference to be valid?

a: No - the Central Limit Theorem applies, which states the sampling distribution is normal for any population distribution.

b: Yes - the population distribution must be normally distributed.

Insert your choice (a or b): .

Answer 1

Part 1

An estimate of the population mean is given by 20.74 (the sample mean).

Part 2

The standard error is 1.85934 ()

Part 3

Under H₀ :

Thus, the distribution is t₃₄.

Part 4

The test statistic has value

Part 5

The test is right tailed thus the rejection region lies in the right tail.

Moreover. the 1% point of t₃₄ distribution (from the right) is 2.44115.

Testing at significance level 0.01, the rejection region is greater than  2.44.

Part 6

Since the test statistic is not in the rejection region, there is no evidence to reject the null hypothesis, H₀.

Part 7

There is insufficient evidence to suggest that the average number of gloves used by all employees per week is greater than 23.

Part 8

b. Yes - the population distribution must be normally distributed.

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