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Chapter 9: Q. 71 (page 588)

Sweetening colas Cola makers test new recipes for loss of sweetness during storage. Trained tasters rate the sweetness before and after storage. From experience, the population distribution of sweetness losses will be close to Normal. Here are the sweetness losses (sweetness before storage minus sweetness after storage) found by tasters from a random sample of 10batches of a new cola recipe:

2.00.40.72.0-0.42.2-1.31.21.12.3

Are these data good evidence that the cola lost sweetness? Carry out a test to help you answer this question.

Short Answer

Expert verified

It appears that there is an average loss of sweetness for this cola.

Step by step solution

01

Given information

Here are the sweetness losses (sweetness before storage minus sweetness after storage) found by tasters from a random sample of 10batches of a new cola recipe:

2.00.40.72.0-0.42.2-1.31.21.12.3

02

Explanation

State: H0:μ=0versusHa:μ<0, where μis the actual mean amount of sweetness loss.

Plan: One-sample t test for μ.

Random: The sample was randomly selected.

Normal: Previous experience tells us that sweetness losses will be close to Normal. Independent: There are at least 100batches of the new soda available.

Do: t=2.70, P-value=0.0122.

Conclude: Since our P-value is less than 0.05, we reject H0.

It appears that there is an average loss of sweetness for this cola.

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Most popular questions from this chapter

You are thinking about opening a restaurant and are searching for a good location. From the research you have done, you know that the mean income of those living near the restaurant must be over $85,000 to support the type of upscale restaurant you wish to open. You decide to take a simple random sample of 50 people living near one potential location. Based on the mean income of this sample, you will decide whether to open a restaurant there.8

(a) State appropriate null and alternative hypotheses. Be sure to define your parameter.

(b) Describe a Type I and a Type II error, and explain the consequences of each.

(c) If you had to choose one of the “standard” significance levels for your significance test, would you choose α=0.01, 0.05, or 0.10? Justify your choice.

You are testing HO:μ=10Hα:μ<10against based on an SRS of 20observations from a Normal population. The tstatistic is . t=-2.25The P-value

(a) falls between 0.01and0.02

(b) falls between0.02and0.04

(c) falls between0.04and0.05

(d) falls between .05and0.25.

(c) is greater than0.25.

Tests and CIs The P-value for a one-sided test of the null hypothesisH0:μ=15is 0.03.

(a) Does the 99%confidence interval for μinclude 15? Why or why not?

(b) Does the 95%confidence interval for μinclude 15? Why or why not?

Which of the following 95% confidence intervals would lead us to reject H0:p=0.30in favor of Ha:p≠0.30at the 5% significance level?

(a) (0.29, 0.38) (c) (0.27, 0.31) (e) None of these

(b) (0.19, 0.27) (d) (0.24, 0.30)

To determine the reliability of experts who interpret lie detector tests in criminal investigations, a random sample of 280such cases was studied. The results were

(a) 15/280.

(b) 9/280.

(c) 15/140.

(d) 9/140.

(e) 15/146.
See all solutions

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