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 1.5 mg is acceptable. A sample of 32 capsules was taken and the weights are provided below:

98.5	98.2	99.6	99.3	96.9
99	98.3	102.8	100.6	103.3
97.3	98.6	101.1	101.7	98.1
101.3	99.7	102.9	101.8	100.9
99.5	99.8	99.5	101.5	98.4
101	98.2	100.8	99.2	102.7
99.3	101.7

(Note: The average and the standard deviation of the data are respectively 100 g and 1.72 g.)

At 10% significance level, test the claim that the standard deviation of capsule weights of the drug is different from 1.5 g.

Procedure: Select an answer

One proportion Z Hypothesis Test

One mean Z Hypothesis Test

One variance χ² Hypothesis Test

One mean T Hypothesis Test

Assumptions: (select everything that applies)

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

Step 1. Hypotheses Set-Up:

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

Step 2. The significance level α= %______

Step 3. Compute the value of the test statistic: Select an answer χ²₀ ,t₀ ,z₀, f₀  = (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 10% significance level we Select an answer (DO ,NOT DO) have sufficient evidence to reject the null hypothesis in favor of the alternative hypothesis.

Answer 1