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.............................. = 0.031
Significance level ……........... = 0.05

The study design is:

a. pre-test/posttest
b. one-sample dependent mean
c. two-sample mean

What numbers are being compared in the test?

a. average difference and zero
b. means
c. standard deviations
d. critical values

Which number from the computer output is compared to the significance level to check if the null hypothesis should be rejected?

a. degrees of freedom
b. test statistic
c. P-value
d. critical value

Answer 1

Answer:

(1) The correct option is (c).

(2) The correct option is (b).

(3) The correct option is (c).

Step-by-step explanation:

The claim made by Gillette is that their double-edge shaver is better than the leading brand of single-edge shavers (Lady Bic).

A random sample of 26 women are selected and are asked to rate the shaver  from both the brands.

The mean difference of the ratings were then compared.

(1)

The experiment performed here has the main purpose of determining whether there is any difference between the ratings of the two shaver, i.e. to determine if one is better than the other.

The two samples are selected independently, since the women rated the shavers independent of each other.

The study design used here is a two-sample mean.

Thus, the correct option is (c).

(2)

The experiment involves testing the mean difference of the two ratings.

So the hypothesis can be defined as:

H₀: There is no difference between the two means, i.e. μ₁ - μ₂ = 0.

Hₐ: There is a difference between the two means, i.e. μ₁ - μ₂ > 0.

*Here 1 denotes the ratings for Gillette shavers and 2 denotes the ratings for Lady Bic.

The parameters that are being compared in this test are the two means.

Thus, the correct option is (b).

(3)

The decision rule of the test is:

If the p-value of the test is less than the significance level (α) then the null hypothesis will rejected. And if the p-value of the test is more than the significance level (α) then the null hypothesis will be failed to be rejected.

Thus, the correct option is (c).