Question

Gillette claims that their double-edge shaver is better than the leading brand of single-edge shavers (Lady Bic). In a recent study, 26 women rated the Gillette and the Lady Bic shavers on smoothness, closeness and safety. One group of women were used and each woman recorded two scores. The mean difference of those scores were tested with the following results.

Critical Value…………… t = 1.645

Test statistic ..................... t = 1.978

P-value.............................. = . 031

Significance level ……........... = .05

What type of conclusion error could be made using the results of this study?

                 a) type II                b)   none            c) type III                            d) type I

Answer 1

Since we have to test if the scores of Gillette are better than those of Lady Bic, the null and alternative hypotheses would be

are the population mean scores of Gillette and Lady Bic respectively

Given

p-value = 0.031

Significance Level = 0.05

0.031 < 0.05

that is, p-value is less than the significance level.

Hence, we reject Ho

Also

for a right tailed test we reject Ho if calculated test statistic > critical value of t

1.978 > 1.645                   

that is calculated test statistic t > critical value of t        

Hence, we reject Ho

A Type I error occurs if we reject Ho when it is true

and a Type II error occurs if we fail to reject Ho when it is false

In the given case, our conclusion is to reject Ho

Thus, there is a probability of rejecting Ho when it is true (This probability is given by the p-value)

Hence, we may make a Type I error

Answer :