Question

The candy Reese's Pieces come in three different colors: orange, yellow, and brown. Less than forty-five percent of the pieces are supposed to be orange. A random sample of Reese's Pieces packages were opened and 166 out of 400 pieces were orange. Test the hypothesis that less than forty-five percent of Reese's Pieces are orange. Use α = .05 (define the population parameter in H0,.State the Ha and Ho,)

1. H0:

2. Ha:

3. Test Statistics (z or t score, indicate which one)

4. Rejection Region for α = .05 (based on the Ha, draw the distribution and rejection region you can use software or draw it by hand and take a picture and insert in document.)

5. Conclusion:

6. Based on your test of hypothesis, which statement would you agree with (choose one)?

__________The percent of Reese's Pieces that are orange is less than forty-five percent.

__________The percent of Reese's Pieces that are orange may be at least forty-five percent.

Answer 1

Solution:

Given:

Claim: Less than forty-five percent of the pieces are supposed to be orange.

A random sample of Reese's Pieces packages were opened and 166 out of 400 pieces were orange.

Thus

n= 400

x = 166

Thus sample proportion is:

α = .05

Part 1)

H0: p 0.45

Part 2)

Ha: p < 0.45

Part 3) Test Statistics:

Part 4)  Rejection Region for α = .05

Since this is left tailed test , Rejection Region would be in left tail.

Thus look in z table for Area = 0.0500 or its closest area and find z value

Area 0.0500 is in between 0.0495 and 0.0505 and both the area are at same distance from 0.0500

Thus we look for both area and find both z values

Thus Area 0.0495 corresponds to -1.65 and 0.0505 corresponds to -1.64

Thus average of both z values is : ( -1.64+ - 1.65) / 2 = -1.645

Thus Z = -1.645

Thus Rejection Region for α = .05 is:

Reject H0, if z test statistic value .

Part 5) Conclusion:

Since z test statistic value = > z critical value = -1.645 , we fail to reject H0.

At 0.05 level of significance , we do not have sufficient evidence to conclude that: less than forty-five percent of Reese's Pieces are orange.

Part 6)

Since we failed to reject H0, we agree with the statement:

The percent of Reese's Pieces that are orange may be at least forty-five percent.