Question

Because library books are read many times, glue is often applied to the spine of a book to keep the pages tight. A glue is considered successful if a book lasts at least 6 months before needing to be reglued. Two brands of glue, G and K, were tested to determine whether there was a difference in the proportion of books lasting at least 6 months. Let pG represent the proportion of books lasting at least 6 months when glued with G, and let pK represent the proportion of books lasting at least 6 months when glued with K. The following hypothesis test was conducted at the significance level of α=0.01
H0: pG= pK
Ha: pG≠pK

All conditions for inference were met, and the resulting p-value was 0.006. Which of the following is the correct decision for the test?

a. The p-value is less than α, and the null hypothesis is rejected. There is not convincing evidence to support the claim that the proportion of books lasting at least 6 months when glued with G is different from the proportion of books lasting at least 6 months when glued with K.
b. The p-value is less than α , and the null hypothesis is rejected. There is convincing evidence to support the claim that the proportion of books lasting at least 6 months when glued with G is different from the proportion of books lasting at least 6 months when glued with K.
c. The p-value is less than α, and the null hypothesis is not rejected. There is not convincing evidence to support the claim that the proportion of books lasting at least 6 months when glued with G is different from the proportion of books lasting at least 6 months when glued with K.
d. The p-value is greater than α, and the null hypothesis is rejected. There is convincing evidence to support the claim that the proportion of books lasting at least 6 months when glued with G is different from the proportion of books lasting at least 6 months when glued with K.
e. The p-value is greater than α, and the null hypothesis is not rejected. There is not convincing evidence to support the claim that the proportion of books lasting at least 6 months when glued with G is different from the proportion of books lasting at least 6 months when glued with K.

Answer 1

Answer:

B) The  p -value is less than  α , and the null hypothesis is rejected. There is convincing evidence to support the claim that the proportion of books lasting at least 6 months when glued with G is different from the proportion of books lasting at least 6 months when glued with K.

Step-by-step explanation:

Since 0.006<0.01, the null hypothesis is rejected. There is convincing statistical evidence that the proportion of books lasting at least 6 months when glued with G is different from the proportion of books lasting at least 6 months when glued with K.

Answer 2

Answer:

a. The p-value is less than α, and the null hypothesis is rejected. There is not convincing evidence to support the claim that the proportion of books lasting at least 6 months when glued with G is different from the proportion of books lasting at least 6 months when glued with K.

Step-by-step explanation:

It is given that the library books are often glued for keeping the pages stick and intake. A glue is considered successful if it is able to make the pages of the book intake for at least six months.

It is given that the value of α is = 0.01

and the value of p is = 0.006

Thus when the p-value is less than the value of α, it results in the null hypothesis to get  rejected. And there is no convincing support claim that the proportion of the books glued with G lasted for 6 months is different from the proportion of the books that lasted for 6 months when it is glued with K brand.