Question

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?

Answer 1

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):

Ho : μ-443

Alternative hypothesis (H₁)

H1 : μ < 443

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

One-Sample T Test of mu 443 vs < 443 98% Upper 28 435.00 29.00 5.48 446.83-1.46 0.078

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