Question

What I have so far is bold.

Question: The Mars company claims that 13 percent of M&M’s plain candies distributed into bags are brown. Investigate this claim with an appropriate hypothesis test. Use a significance level of α = 0.05.

1. What is the parameter of interest in this situation? Brown M&Ms = .13

2. Null hypothesis: Ho: p= .13

3. Alternative hypothesis: Ha: p does not = .13

4.

Color	Count
Brown	7
Non-Brown	49
Total	56

5. What test should we use for this hypothesis?

6. Briefly explain the process of performing the hypothesis test with the TI calculator.

7. The p-value for this test statistic is: _______________.

8. Conclusion: We REJECT/DO NOT REJECT the null hypothesis. (Circle the correct answer)

9. State what this conclusion means in terms of the problem.

Answer 1

n= 56, x= 7, P = 0.13, =0.05

Ho: P = 0.13

H1: P 0.13

for this hypothesis test we are using one sample proportion z test

Steps to calculate using TI-83 Calculator

1) Press button STAT

2) then press right arrow key two times to navigate to TESTS

3) then simply scroll down to 1- PropZTest

4) then Enter data as

P0 : 0.13

x : 7

n : 56

5) select Prop 0 then press button ENTER

6) Then simply scroll down to Calculate and press button ENTER

you will get answer as follows:

Calculate test statistics

  

where,

z = -0.11125

test statistics(z) = -0.11

Calculate P-value

P-value= 2* P(z< -0.11)

Calculate  P(z< -0.11) using normal z table we get,

P(z< -0.11) = 0.4562

P-value= 2*0.4562

P-value= 0.9124

Decision Rule:

if (P-Value)   ( ) then reject Ho

if (P-Value) > ( ) then do not reject Ho

Since (P-Value= 0.9124) > ( =0.05)

failed to reject Null hypothesis (Ho).

Therefore, there is enough evidence to claim that the 13 percent of M&M’s plain candies distributed into bags are brown at  α=0.05 significance level.