Question

A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 441 gram setting. Based on a 19 bag sample where the mean is 448 grams and the standard deviation is 27 grams, is there sufficient evidence at the 0.01 level that the bags are overfilled?

Step 1. Enter the hypotheses:

Step 2. Enter the value of the t test statistic.

Step 3. Specify if the test is one-tailed or two-tailed.

Step 4. Enter the decision rule.
Reject H0 if t >

Step 5. Enter the conclusion.
Reject Null Hypothesis
Fail to Reject Null Hypothesis

Answer 1

Conclusion: Fail to Reject Null Hypothesis

We conclude that the bags are not overfilled.

Explanation:

We are given the following in the question:

Population mean, μ = 441 gram

Sample mean,
`\bar{x}` = 448 gram

Sample size, n = 19

Alpha, α = 0.01

Sample standard deviation, s = 27 grams

First, we design the null and the alternate hypothesis

`H_(0): \mu = 441\text{ grams}\\H_A: \mu > 441\text{ grams}`

We use One-tailed t test to perform this hypothesis.

Formula:

`t_(stat) = \displaystyle\frac{\bar{x} - \mu}{(s)/(√(n)) }` Putting all the values, we have

`t_(stat) = \displaystyle(448 - 441)/((27)/(√(19)) ) = 1.13`

Now,

`t_(critical) \text{ at 0.01 level of significance, 18 degree of freedom } = 2.55`

Since,

`t_(stat) < t_(critical)`

We reject null hypothesis when t > 2.55

We accept the null hypothesis and fail to reject it. Thus, we conclude that the bags are not overfilled.