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Chapter 11: Q 9. (page 718)

Munching Froot Loops Kellogg鈥檚 Froot Loops cereal comes in six colors:

orange, yellow, purple, red, blue, and green. Charise randomly selected 120 loops and noted the color of each. Here are her data:

Do these data provide convincing evidence at the 5% significance level that Kellogg鈥檚 Froot Loops do not contain an equal proportion of each color?

Short Answer

Expert verified

There is insufficient evidence to refute Kellogg's assertion that its Froot Loop includes an equal quantity of each flavor.

Step by step solution

01

Given information

Significance level: 5% = 0.05

02

Concept

Null hypothesis: H0

When the value of P is less than or equal to the significance level, the null hypothesis is rejected.

03

Explanation

The Pvalue is used to calculate the likelihood of a test statistic or a more extreme number.

The P-value in the appendix, which contains the X2value in the row df=5may be found in the chi-square distribution table.

0.15<P<0.20

When the value of Pis not less than or equal to the significance level, the null hypothesis is not rejected.

P>0.05: fail to reject H0

Hence, There is insufficient evidence to disprove the company's assertion that Kellogg's produces Froot Loop.

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Most popular questions from this chapter

No chi-square A school鈥檚 principal wants to know if students spend about the same amount of time on homework each night of the week. She asks a random sample of 50 students to keep track of their homework time for a week. The following table displays the average amount of time (in minutes) students reported per night.

Explain carefully why it would not be appropriate to perform a chi-square test for goodness of fit using these data.

The manager of a high school cafeteria is planning to offer several new types of food for student lunches in the new school year. She wants to know if each type of food will be equally popular so she can start ordering supplies and making other plans. To find out, she selects a random sample of 100students and asks them, 鈥淲hich type of food do you prefer: Ramen, tacos, pizza, or hamburgers?鈥� Here are her data:

The P-value for a chi-square test for goodness of fit is 0.0129. Which of the following is the most appropriate conclusion at a significance level of 0.05?

a. Because 0.0129 is less than 伪=0.05 reject H0 . There is convincing evidence that the food choices are equally popular.

b. Because 0.0129 is less than 伪=0.05 reject H0 There is not convincing

evidence that the food choices are equally popular.

c. Because 0.0129 is less than 伪=0.05 reject H0 . There is convincing evidence that the food choices are not equally popular.

d. Because 0.0129 is less than 伪=0.05 fail to reject H0 There is not convincing evidence that the food choices are equally popular.

e. Because 0.0129 is less than 伪=0.05 fail to reject H0 There is convincing

evidence that the food choices are equally popular.

A random sample of traffic tickets given to motorists in a large city is examined. The tickets are classified according to the race or ethnicity of the driver. The results are summarized in the following table.

The proportion of this city's population in each of the racial/ethnic categories listed is as follows.

We wish to test H0: The racial/ethnic distribution of traffic tickets in the city is the same as the racial/ethnic distribution of the city's population.

We compute the value of the 蠂2test statistic to be 6.57. Assuming that the conditions for inference are met, which of the following is the correct P-value?

a. Greater than0.20

b. Between 0.10and0.20

c. Between 0.05and0.10

d. Between 0.01and0.05

e. Less than0.01

How to quit smoking Refer to Exercise 37. Which treatment seems to be most effective? Least effective? Justify your choices.

Last python Refer to Exercises 28 and 30.

a. Verify that the conditions for inference are met.

b. Use Table C to find the P-value. Then use your calculator鈥檚 蠂2 cdf command.

c. Interpret the P-value from the calculator.

d. What conclusion would you draw using 伪=0.10?
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