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Chapter 9: Q.71 (page 588)

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 10 batches of a new cola recipe:

2.0 0.4 0.7 2.0 0.4 2.2 1.3 1.2 1.1 2.3

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

Short Answer

Expert verified

These data are good evidence that the cola lost sweetness

Step by step solution

01

Introduction

The scientific strategy requires that one can test it. Scientists for the most part base scientific speculations on previous observations that can't satisfactorily be explained with the available scientific theories.

A random sample of 10 batches of a new cola recipe:

2.00.40.72.00.42.21.31.22.3

02

Explanation

The significance level is 0.05

Calculating the null and alternative hypotheses,

H0:μ=0Ha:μ>0

Using a calculator we find the p-value.

The p-value is less than the significance level and the null hypothesis is dismissed.

Hence these data are good evidence that the cola lost sweetness.

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Most popular questions from this chapter

Normal body temperature (8.2) If "normal" body temperature really is 98.6F, we would expect the proportion pof all healthy 18- to 40 -year-olds who have body temperatures less than this value to be 0.5. Construct and interpret a 95% confidence interval for p. What conclusion would you draw?

Improving health A large company's medical director launches a health promotion campaign to encourage employees to exercise more and eat better foods. One measure of the effectiveness of such a program is a drop in blood pressure. The director chooses a random sample of 50employees and compares their blood pressures from physical cams given before the campaign and again a year later. The mean change (after - before) in systolic blood pressure for these 50employees is -6and the standard deviation is 19.8.

(a) Do these data provide convincing evidence of an average decrease in blood pressure among all of the company's employees during this year? Carry out a test at the α=0.05significance level.

(b) Can we conclude that the health campaign caused a decrease in blood pressure? Why or why not?

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.

Ages of presidents Joe is writing a report on the backgrounds of American presidents. He looks up the ages of all the presidents when they entered office. Because Joe took a statistics course, he uses these numbers to perform a significance test about the mean age of all U.S. presidents. Explain why this makes no sense.

Spinning for apples (6,3 or 7.3) In the "Ask Marilyn" column of Parade magzine, a reader posed this question: "Say that a slot machine has five wheels, and each wheel has five symbols: an apple, a grape, a peach, a pear, and a plum. I pull the lever five times. What are the chances that I'll get at least one apple?" Suppose that the wheels spin independently and that the fre symbols are equally likely to appear on each wheel in a given spin.

(a) Find the probability that the slot player gets at least one apple in one pull of the lever. Show your method clearly.

(b) Now answer the reader's question. Show your method clearly.
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