Question

For a certain drug, based on standards set by the United States Pharmacopeia (USP) - an official public standards-setting authority for all prescription and over-the-counter medicines and other health care products manufactured or sold in the United States, a standard deviation of capsule weights of less than 0.8 mg is acceptable. A sample of 20 capsules was taken and the weights are provided below:

120.3	120.8	120.1	119.7	120.8
119.4	119.1	120.9	118.9	119.5
120.4	121.1	118.6	119.4	119.3
119.8	120.2	119.5	118.9	119.8

(Note: The average and the standard deviation of the data are respectively 119.8 g and 0.73 g.)

At 5% significance level, test the claim that the standard deviation of capsule weights of the drug is different from 0.8 g.

Procedure: Select an answer One mean Z Hypothesis Test One mean T Hypothesis Test One proportion Z Hypothesis Test One variance χ² Hypothesis Test

Assumptions: (select everything that applies)

• Normal population
• Sample size is greater than 30
• The number of positive and negative responses are both greater than 10
• Population standard deviation is unknown
• Population standard deviation is known
• Simple random sample

Step 1. Hypotheses Set-Up:

H0:H0: Select an answer p σ² μ  =	, where ? p μ σ  is the Select an answer population proportion population standard deviation population mean  and the units are ? lbs g mg kg
Ha:Ha: Select an answer μ p σ²  ? > ≠ <	, and the test is Select an answer Right-Tail Left-Tail Two-Tail

Step 2. The significance level α=α= %

Step 3. Compute the value of the test statistic: Select an answer z₀ f₀ χ²₀ t₀  = (Round the answer to 3 decimal places)

Step 4. Testing Procedure: (Round the answers to 3 decimal places)

CVA	PVA
Provide the critical value(s) for the Rejection Region:	Compute the P-value of the test statistic:
left CV is  and right CV is	P-value is

Step 5. Decision:

CVA	PVA
Is the test statistic in the rejection region?	Is the P-value less than the significance level?
? yes no	? yes no

Conclusion: Select an answer Do not reject the null hypothesis in favor of the alternative. Reject the null hypothesis in favor of the alternative.

Step 6. Interpretation:

At 5% significance level we Select an answer DO DO NOT  have sufficient evidence to reject the null hypothesis in favor of the alternative hypothesis.

Answer 1