Question

Question 1 options:

As Quality Control Inspector, you have previously believed a claim that 3.2% of items made on your production line are defective.

A.) To see if you should still believe this claim: You decide to do a two-sided significance test, with a significance level of 2%.

You then randomly sample 420 items from the production line, and find that 22 of the items are defective.

In percentage form, and rounded to four digits past the decimal point: What is the approximate P-value of your test?

Include a percentage symbol at the end of your numerical answer (with no spaces).

B.) As Quality Control Inspector, you have previously believed a claim that 3.2% of items made on your production line are defective.

To see if you should still believe this claim: You decide to do a two-sided significance test, with a significance level of 2%.

You then randomly sample 420 items from the production line, and find that 22 of the items are defective.

Which of the following are correct general statements about the conclusion that you find from your significance test?

(Select all that apply. To be marked correct: All of the correct selections must be made, with no incorrect selections.)

	Your sample results are statistically significant.
	You reject the null hypothesis in favor of the two-sided alternative.
	Your sample results are not statistically significant.
	The P-value from your test, is less than or equal to your chosen alpha-value.
	Based upon the evidence from your significance test, you should no longer believe the null hypothesis claim.
	You fail to reject the null hypothesis.
	Based upon the evidence from your significance test, you have no reason to stop believing the null hypothesis claim.
	The P-value from your test, is greater than your chosen alpha-value.

C.) In a marketing campaign: A soda producer claims that 10% of all the soda bottles they continuously produce, have a winning message under the bottle cap ("winning caps").

Over a given three-month summer, during the soda producer's marketing campaign: You purchase 150 bottles of this soda, and collect the bottle caps in a bag without yet looking at them. To see if you should believe the soda producer's claim about the total proportion of winning caps, you decide to do a two-sided significance test, with an alpha-value of 1%.

You then inspect all 150 of the bottle caps you've collected, and find that 6 of them are winning caps.

In percentage form, and rounded to four digits past the decimal point: What is the approximate P-value of your test?

Include a percentage symbol at the end of your numerical answer (with no spaces).

D.) In a marketing campaign: A soda producer claims that 10% of all the soda bottles they continuously produce, have a winning message under the bottle cap ("winning caps").

Over a given three-month summer, during the soda producer's marketing campaign: You purchase 150 bottles of this soda, and collect the bottle caps in a bag without yet looking at them. To see if you should believe the soda producer's claim about the total proportion of winning caps, you decide to do a two-sided significance test, with an alpha-value of 1%.

You then inspect all 150 of the bottle caps you've collected, and find that 6 of them are winning caps.

Which of the following are correct general statements about the conclusion that you find from your significance test?

(Select all that apply. To be marked correct: All of the correct selections must be made, with no incorrect selections.)

	You reject the null hypothesis in favor of the two-sided alternative.
	Your sample results are statistically significant.
	Based upon the evidence from your significance test, you have no reason to stop believing the null hypothesis claim.
	Based upon the evidence from your significance test, you should no longer believe the null hypothesis claim.
	Your sample results are not statistically significant.
	The P-value from your test, is less than or equal to your chosen alpha-value.
	The P-value from your test, is greater than your chosen alpha-value.
	You fail to reject the null hypothesis.

Answer 1

A.

Sample proportion:

Hypothesis:

Test statistic,

P-value = 2 * P( z > 2.357 ) = 0.0175 = 1.75%

Since p-value is less than 2%, we reject null hypothesis.

B.

Your sample results are statistically significant.

You reject the null hypothesis in favour of the two-sided alternative.

The P-value from your test, is less than or equal to your chosen alpha-value.

Based upon the evidence from your significance test, you should no longer believe the null hypothesis claim.

C.

Sample proportion:

Hypothesis:

Test statistic,

P-value = 2 * P( z < -2.45 ) = 0.0143 = 1.43%

Since p-value is less than 2%, we reject null hypothesis.

D.

You reject the null hypothesis in favour of the two-sided alternative.

Your sample results are statistically significant.

Based upon the evidence from your significance test, you should no longer believe the null hypothesis claim.

The P-value from your test, is less than or equal to your chosen alpha-value.