(1 pt) A cracker bakery wants to test microwaving crackers after breaking to red
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Question
(1 pt) A cracker bakery wants to test microwaving crackers after breaking to reduce the risk of broken crackers at the time the package is opened.
The experimenter randomly assigns 65 crackers from one day's production to be microwaved after baking, and another 65 to a control group. Fourteen days later, 3 of the microwaved crackers show visible "checking", which is the starting point for breaks. At the same time, 57 of the 65 crackers in the control group show signs of checking.
Do these samples provide evidence significant at the 0.1% level that microwaving after baking reduces the risk of checking in these crackers?
Formulate H0 and Ha.
a. Give the test statistic:
b. Give the P-value:
c. Your decision for the hypothesis test:
A. Do Not Reject Ha.
B. Reject H0.
C. Reject Ha.
D. Do Not Reject H0.
Explanation / Answer
Two sample z test for the population proportion
A cracker bakery wants to test microwaving crackers after breaking to reduce the risk of broken crackers at the time the package is opened.
The experimenter randomly assigns 65 crackers from one day's production to be microwaved after baking, and another 65 to a control group. Fourteen days later, 3 of the microwaved crackers show visible "checking", which is the starting point for breaks. At the same time, 57 of the 65 crackers in the control group show signs of checking.
Do these samples provide evidence significant at the 0.1% level that microwaving after baking reduces the risk of checking in these crackers?
Formulate H0 and Ha.
Here, we have to use the two sample z test for the population proportion.
The null and alternative hypothesis for this two sample z test is given as below:
Null hypothesis: H0: There is no any significant difference in the proportion of the signs of checking for the crackers in the microwave and another control group.
Alternative hypothesis: Ha: The proportion of the signs of checking for the crackers in the microwave is less than the proportion of the signs of checking for control group.
H0: P1 = P2 versus Ha: P1 < P2
Test statistic = z = -9.5
P-value = 0.00
We reject the null hypothesis H0 because p-value is less than the given level of significance or alpha value 0.05. This means we reject the null hypothesis that there is no any significant difference in the proportion of the signs of checking for the crackers in the microwave and another control group. This means the proportion of the signs of checking for the crackers in the microwave is less than the proportion of the signs of checking for control group. Therefore, we concluded that microwaving after baking reduces the risk of checking in these crackers.
The test is given as below:
Z Test for Differences in Two Proportions
Data
Hypothesized Difference
0
Level of Significance
0.05
Group 1
Number of Items of Interest
3
Sample Size
65
Group 2
Number of Items of Interest
57
Sample Size
65
Intermediate Calculations
Group 1 Proportion
0.046153846
Group 2 Proportion
0.876923077
Difference in Two Proportions
-0.83076923
Average Proportion
0.4615
Z Test Statistic
-9.5004
Lower-Tail Test
Lower Critical Value
-1.6449
p-Value
0.0000
Reject the null hypothesis
Z Test for Differences in Two Proportions
Data
Hypothesized Difference
0
Level of Significance
0.05
Group 1
Number of Items of Interest
3
Sample Size
65
Group 2
Number of Items of Interest
57
Sample Size
65
Intermediate Calculations
Group 1 Proportion
0.046153846
Group 2 Proportion
0.876923077
Difference in Two Proportions
-0.83076923
Average Proportion
0.4615
Z Test Statistic
-9.5004
Lower-Tail Test
Lower Critical Value
-1.6449
p-Value
0.0000
Reject the null hypothesis
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