
Concept explainers
Heinz, a manufacturer of ketchup, uses a particular machine to dispense 16 ounces of its ketchup into containers. From many years of experience with the particular dispensing machine, Heinz knows the amount of product in each container follows a
- (a) State the null hypothesis and the alternate hypothesis.
- (b) What is the
probability of a Type I error? - (c) Give the formula for the test statistic.
- (d) State the decision rule.
- (e) Determine the value of the test statistic.
- (f) What is your decision regarding the null hypothesis?
- (g) Interpret, in a single sentence, the result of the statistical test.
a.

State the hypotheses.
Answer to Problem 1SR
The null hypothesis is
The alternative hypothesis is
Explanation of Solution
Here, the claim is that there is evidence that the mean amount dispensed is different from 16 ounces. This defines the alternative hypothesis.
Let
The hypotheses are given below:
Null hypothesis:
Alternative hypothesis:
b.

Write the probability of a Type I error
Explanation of Solution
Type I error:
Probability of rejecting
Here, the null hypothesis is rejected. But in actual the mean amount dispensed is 16 ounces.
c.

Write the formula for the test statistic.
Explanation of Solution
The formula for the test statistic is given below:
Where,
d.

Write the decision rule.
Explanation of Solution
Step-by-step procedure to obtain the critical value using MINITAB:
- Choose Graph > Probability Distribution Plot choose View Probability > OK.
- From Distribution, choose ‘Normal’ distribution.
- Click the Shaded Area tab.
- Choose Probability and Both Tail for the region of the curve to shade.
- Enter the Probability value as 0.05.
- Click OK.
Output using the MINITAB software is given below:
From the output, the critical value is ±1.96.
Decision rule:
If
If
e.

Find the value of test statistic.
Answer to Problem 1SR
The value of test statistic is 0.8.
Explanation of Solution
Step by step procedure to obtain the test statistic using MINITAB software is given below:
- Choose Stat > Basic Statistics > 1-Sample Z.
- In Summarized data, enter the sample size as 50 and mean as 16.017.
- In Standard deviation, enter 0.15.
- Check Options, enter Confidence level as 95.
- In Perform Hypothesis test, enter 16 Under Hypothesized mean.
- Choose Mean ≠ Hypothesized mean in alternative.
- Click OK in all dialogue boxes.
Output using the MINITAB software is given below:
From the MINITAB output, the value of test statistic is 0.8.
f.

Find the decision.
Answer to Problem 1SR
The decision is that fail to reject the null hypothesis.
Explanation of Solution
Decision:
Here, the computed z-value is 0.8.
The computed z-value lies between ±1.96.
From the decision rule, fail to reject the null hypothesis.
g.

Write the single sentence for the result of the test.
Explanation of Solution
The null hypothesis is not rejected. Hence, it can be concluded that there is no evidence that the mean amount dispensed is different from 16 ounces.
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Chapter 10 Solutions
Statistical Techniques in Business and Economics
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