A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 443 gram setting. It is believed that the machine is underfilling the bags. A 28 bag sample had a mean of 435 grams with a standard deviation of 29. Assume the population is normally distributed. Is there sufficient evidence at the 0.02 level that the bags are underfilled?
Here we want to test "whether there is sufficient evidence to infer at the 2% significance level that the bags are underfilled ."
Let's write null and alternative hypothesis from the above statement.
Null hypothesis (H0):
Alternative hypothesis (H1)
Using Minitab:
n = sample size = 28
= sample mean = 435
s = sample standard deviation = 29
Step 1) Click on Stat>>>Basic Statistics >>1 sample t...
Step 2) Select summarized data
Sample size : 28
Mean:435
Standard deviation : 29
then click on Perform hypothesis test enter hypothesis mean ( 27)
Step 3)then click on Option select level of confidence = 1 - = 1 - 0.02 = 0.98
So put it as 98
Alternative " less than"
Click on OK
again Click on Ok
So we get the following output
From the above minitab output
t test statistic = T = -1.46
P-value = 0.078
Decision rule:
1) If p-value < level of significance (alpha) then we reject null hypothesis
2) If p-value > level of significance (alpha) then we fail to reject null hypothesis.
Here p value = 0.078 > 0.02 so we used 2nd rule.
That is we fail to reject null hypothesis
Conclusion: At 2% level of significance there are not sufficient evidence to say that the sample data indicates that the bags are underfilled
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