Question

A medical  company is checking their drugs medicines according to the regulations imposed. The company must ensure that their medicine contains exactly the amount prescribed. For a certain pill they tested they require the pill to be 20mg. The random sample of 18 that they took revealed that this was not the case. The mean weight of the pills in the sample was 22.07mg with a standard deviation of 5.90mg.
Use α = 0.1 to answer the following questions.

a)

What type of test would be appropriate in this situation?

	A right-tailed test. H0: μ≤20, H1: μ>20.
	A left-tailed test. H0: μ≥20, H1: μ<20.
	A two-tailed test. H0: μ=20, H1: μ≠20.
	None of the above.

b)

Which of the following sounds like an appropriate decision rule?

	Reject H0 in favour of H1 if the computed value of the test statistic is greater than 1.74
	Reject H0 in favour of H1 if the computed value of the test statistic is less than -1.74 or greater than 1.74
	Reject H0 in favour of H1 if the computed value of the test statistic is between -1.74 and 1.74
	Reject H0 in favour of H1 if the computed value of the test statistic is less than -1.74
	None of the above

c) What is the computed test statistic?
For full marks your answer should be accurate to at least two decimal places.

Test statistic: 0

d)

Based on your computed test statistic and the decision rule you have decided upon, what can we conclude about H₀?

	There is sufficient evidence, at the given significance level, to reject H0.
	There is insufficient evidence, at the given significance level, to reject H0; or we fail to reject H0.
	There is insufficient evidence to make it clear as to whether we should reject or not reject the null hypothesis.

e) Round your computed test statistic to two decimal places and find the P-value.
For full marks your answer should be accurate to at least three decimal places.

P-value: 0

Answer 1

Given:

n=18

a) Hypothesis:

A two-tailed test.

H0: μ=20, vs

H1: μ≠20.

b)

t-tabulated=1.74

Reject H0 in favour of H1 if the computed value of the test statistic is less than -1.74 or greater than 1.74

c)Test statistics:

d)

Here l t-calculated l (1.94) > t-tabulated (1.74)

So we reject H0 at 1% level of significance.

Hence,

There is sufficient evidence, at the given significance level, to reject H0.

e)

p-value is 0.001

Which is less than 0.01 so we reject H0 at 1% level of significance.