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Chapter 11: Q. 2.4 (page 684)

Let鈥檚 continue our analysis of Joey鈥檚 sample of M&M鈥橲 Peanut Chocolate Candies from the previous Check Your Understanding (page 681).

4. What conclusion would you draw about the company鈥檚 claimed color distribution for M&M鈥橲 Peanut Chocolate Candies? Justify your answer.

Short Answer

Expert verified

We reject the null hypothesis and accept the alternative one.

Step by step solution

01

Given

23% each of blue and orange, 15% each of green and yellow, and 12% each of red and brown. Joey bought a bag of Peanut Chocolate Candies and counted the colors of the candies in his sample: 12 blue, 7 orange, 13 green, 4 yellow, 8 red, and 2 brown.

02

Interpretation

From previous sub-part we get,p-value鈮�0.048456

Since we have

p-value鈮�0.048456>饾泜=0.05

The result is statistically significant.

We can reject the null hypothesis and accept the alternative.

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Most popular questions from this chapter

Orange, lemon, cherry, raspberry, blueberry, and lime are among the six fruit flavours available in Kellogg's Froot Loops cereal. Charise counted the number of cereal pieces in each flavour as she poured out her morning bowl of cereal. Here are her statistics.

Test the null hypothesis that each flavour of Kellogg's Froot Loops is distributed evenly throughout the population. Perform a follow-up analysis if you discover a noteworthy result.

The General Social Survey asked a random sample of adults, 鈥淒o you favour or oppose the death penalty for persons convicted of murder?鈥� The following table gives the responses of people whose highest education was a high school degree and of people with a bachelor鈥檚 degree:

We can test the hypothesis of 鈥渘o difference鈥� in support for the death penalty among people in these educational categories in two ways: with a two-sample z test or with a chi-square test.

(a) Minitab output for a chi-square test is shown below. State appropriate hypotheses and interpret the P-value in context. What conclusion would you draw? Chi-Square Test: C1, C2 Expected counts are printed below-observed counts Chi-Square contributions are printed below expected counts

(b) Minitab output for a two-sample z test is shown below. Explain how these results are consistent with the test in part (a).

A study of identity theft looked at how well consumers protect themselves from this increasingly prevalent crime. The behaviors of 61randomly selected college students were compared with the behaviors of 59randomly selected non students.39One of the questions was 鈥淲hen asked to create a password, I have used either my mother鈥檚 maiden name, or my pet鈥檚 name, or my birth date,

or the last four digits of my social security number, or a series of consecutive numbers.鈥� For the students, 22agreed with this statement while 30of the nonstudents agreed.

a) Display the data in a two-way table and perform

the appropriate chi-square test. Summarize the results.

(b) Reanalyze the data using the methods for comparing two proportions that we studied in Chapter10. Compare the results and verify that the chi-square

statistic is the square of the z statistic.

How is the hatching of water python eggs influenced by the temperature of the snake鈥檚 nest? Researchers randomly assigned newly laid eggs to one of three water temperatures: hot, neutral, or cold. Hot duplicates the extra warmth provided by the mother python, and cold duplicates the absence of the mother. Here are the data on the number of eggs and the number that hatched

(a) Make a two-way table of temperature by outcome (hatched or not). Calculate the proportion of eggs in each group that hatched. The researchers believed that eggs would not hatch in cold water. Do the data support that belief?

(b) Are the differences between the three groups statistically significant? Give appropriate evidence to support your answer

An appropriate null hypothesis to test whether the trees in the forest are randomly distributed is

(a) H0:渭=25, where 渭=the mean number of trees in each quadrant.

(b) H0:p=0.25, where p=the proportion of all trees in the forest that are in Quadrant 1.

(c) H0:n1=n2=n3=n4=25, where niis the number of trees from the sample in Quadrant i.

(d) H0:p1=p2=p3=p4=0.25, where piis the actual proportion of trees in the forest that are in Quadrant i.

(e) H0:p^1=p^2=p^3=p^4=0.25, where p^iis the proportion of trees in the sample that are in Quadranti.
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