26. Consider the hypothesis test given by

26. Consider the hypothesis test given by
Ho ? = 530
H1 ? ? 530
In a random sample of 225 subjects, the sample mean is found to be 525. Also, the population standard deviation is ?= 25. (20 pts)

Determine the test statistic.
____________

Determine the P-value for this test?
____________

Is there sufficient evidence to justify the rejection of Ho at ?= 0.01 level?
a) No. The Null Hypothesis cannot be rejected. There is insufficient evidence to support the claim.
b) Yes. The Null Hypothesis can be rejected. There is sufficient evidence to support the claim.

c) There is insufficient evidence to make a decision.

27. A researcher thinks that the proportion of women who say that the earth is getting warmer
is greater than the proportion of men. The researcher conducted a survey and found the following results: (25 pts)
In a random sample of 250 women, 70% said that the earth is getting warmer.
In a random sample of 200 men, 67% said that the earth is getting warmer.
Assume we want to use a 0.05 significance to test the claim.

Identify the Null Hypothesis?
_____________
Identify the Alternate Hypothesis?
_____________
Determine the test statistic?
_____________
Determine the critical value?
_____________

Is there sufficient evidence to support the claim that the proportion of women saying the earth is getting warmer is higher than the proportion of men saying the earth is getting warmer?

No. The Null Hypothesis cannot be rejected.
Yes. The Null Hypothesis can be rejected.
The test results are inconclusive.

Refer to the following data for Questions 28 and 29.

X 0 – 1 1 2 4
Y 3 – 2 4 6 8

28. Find an equation of the least squares regression line. (15 pts)
What is the Y intercept of the equation?
_____________
What is the slope of the equation?

_____________
Y = ______ + ______x

Answer the following questions to receive full credit for this problem.
?x = _______, ?y = _______, ?x2 = _______, ?xy = _______
29 Based on the equation from # XXXXX what is the predicted value of y if x=3? (10 pts)

30. The UMUC Daily News reported that the color distribution for plain M&M’s was: 35% brown, 20% yellow, 20% orange, 15% green, and 10% tan. Each piece of candy in a random sample of 100 plain M&M’s was classified according to color, and the results are listed below.

Color Brown Yellow Orange Green Tan
Number 42 21 15 9 13

Assume we want to use a 0.10 significant level to test the claim that the published color distribution is correct. (25 pts)

What is the Null Hypothesis?
__________________

What is the Alternate Hypothesis?
__________________

What is the appropriate distribution for performing this test?

z t Chi Square Uniform

Determine the degrees of freedom for this Hypothesis test?

__________________
Determine the test statistic?

__________________
Determine the critical value?

__________________

Is there sufficient evidence to support the claim that the published color distribution is correct at an alpha of 0.10?

No. The Null Hypothesis cannot be rejected.
Yes. The Null Hypothesis can be rejected.
The test results are inconclusive.

31. Identify the type of sampling used (random, systematic, convenience, stratified, or cluster sampling) in the situation described below. (1 pt)

A woman experienced a tax audit. The tax department claimed that the woman was audited because she was randomly selected from all taxpayers.

What type of sampling did the tax department use?