Question

A company makes cream (for face and hand) bottles that contain a mean amount of therapy cream of 650 ml per bottle as indicated on the label. To monitor its quality, the company randomly selected 100 bottles from the production line and the sample mean amount of cream was 640 ml per bottle. Assume that the amount of cream follows a normal distribution with a standard deviation of 4 ml . Is there evidence at 0.01 level of significance to conclude that the population mean amount of cream is not 650 ml per bottle? Use the confidence interval approach

Answer 1

GIVEN:

Sample size

Sample mean amount of cream

Sample standard deviation

HYPOTHESIS:

The hypothesis is given by,

(That is, the population mean amount of cream is not significantly different from 650 ml per bottle.)

(That is, the population mean amount of cream is significantly different from 650 ml per bottle.)

LEVEL OF SIGNIFICANCE:

99% CONFIDENCE INTERVAL FOR POPULATION MEAN:

FORMULA USED:

The formula for 99% confidence interval for population mean is,

where is the t critical value with degrees of freedom at 99% confidence level.

CRITICAL VALUE:

The two tailed (since ) t critical value with degrees of freedom at significance level is .

CALCULATION:

The 99% confidence interval for the population mean amount of cream is,

Thus the 99% confidence interval for the population mean amount of cream is .

CONCLUSION:

The 99% confidence interval for the population mean amount of cream is .Since the value specified by the null hypothesis () is not in the interval , the null hypothesis can be rejected at the significance level . Thus there is sufficient evidence to prove that the population mean amount of cream is significantly different from 650 ml per bottle.