Question

A dry cleaning establishment claims that a new spot remover will remove more than 75% of the spots to which it is applied. To check this claim, the spot remover will be used on 17 spots chosen at random. If fewer than 13 of the spots are removed, we shall not reject the null hypothesis that p = 0.75; otherwise, we conclude that p > 0.75

(a) State the critical region by filling in the blanks with the appropriate response (based on the options given): We will Blank #1 the null hypothesis if Blank #2 of the spots are removed. Blank #1 Options:

• Not Reject • Reject Blank #2 Options:

• < 12 • < 13   • < 14

• ≤ 12   • ≤ 13   • ≤ 14

• > 12   • > 13   • > 14

• ≥ 12.   • ≥ 13. • ≥ 14

(b) Based on your critical region stated above, if 16 spots are removed, will you reject or not reject the null hypothesis? (c) Based on your critical region stated above, if 9 spots are removed, will you reject or not reject the null hypothesis?

(d) In the following sentence, determine the correct sign (, ≥) that would go in the empty box: If we were to use p-value’s to make our decisions, you would reject the null hypothesis if the p-value blank α.

Answer 1

In the question, the critical region to accept or reject the null hypothesis has already been given.

The null hypothesis is

And the condition to accept the null hypothesis is to have fewer than 13 spots removed.

The alternate hypothesis is

And the condition to reject the null hypothesis is to have greater than or equal to 13 spots removed.

a)  We will ACCEPT the null hypothesis if of the spots are removed.

We will REJECT the null hypothesis if of the spots are removed.

b) Based on the critical region, if 16 spots are removed, we will reject the null hypothesis because

c) Based on the critical region, if 9 spots are removed, we will accept the null hypothesis because .

d) We reject the null hypothesis if it's p-value is significant. A p-value becomes significant if it is less than the significance level .

Hence, we would reject the null hypothesis if the P-Value < . A P value less than is statistically significant because it shows that there is less than probability of the null hypothesis being correct.

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