Question

1. A consumer products company is formulating a new shampoo and is interested in foam height (in millimeters). Foam height is approximately Normally distributed and has a true standard deviation of σ=25 millimeters. The company wishes to test if the true mean foam height exceeds 175 millimeters for the new shampoo. They took a sample of 15, and the sample average was found to be 185 millimeters.

2. What is the type of statistical test procedure that should be used to test the hypotheses? Explain.

  

3. Construct a 95% confidence interval. Test the hypotheses using the confidence interval. Interpret the test result clearly.                                                                                                                                                                    

                    

4. Test the hypotheses using the Test Statistic / Critical Value method (you must clearly indicate the test statistic, and the critical value(s) used). Do you get the same answer as part (c)? If your answer is the same as (c), you do not have to interpret again. Otherwise, interpret the test findings.                              

5. What is the P value of the test? Test the hypotheses using the P value. Do you get the same answer as parts (c) and (d)? If your answer is the same as (c) and (d), you do not have to interpret again. Otherwise, interpret the test findings.                                                                                                                             

Answer 1

Here in this scenario our claim is that the true mean foam height exceeds 175 millimeters for the new shampoo.

a) To test this claim we have to use one sample z test because here the population standard deviations is known to be 25 millimetres.

Now, using the z test we performed the Hypothesis test at 0.05 level of significance as below,

The z critical value is calculated using Standerd normal z-table or using Excel.

The 95% Confidence Interval for population mean is 172.348 millimetres & 197.652 millimetres.

a) From the above test we have the p value is 0.0607,

Conclusion: since p value is greater than alpha level of significance 0.05 so we fail to Reject Ho null hypothesis and concluded that there is not sufficient evidence to support claim that the true mean foam height is exceeding 175 millimetres.

At 0.05 level of significance our result is not significant.

Thank you.