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Chapter 10: Q 6. (page 639)

Broken crackers We don’t like to find broken crackers when we open the package. How can makers reduce breaking? One idea is to microwave the crackers for 30seconds right after baking them. Randomly assign 65newly baked crackers to the microwave and another 65to a control group that is not microwaved. After 1day, none of the microwave group were broken and 16of the control group were broken. Let p1be the true proportions of crackers like these that would break if baked in the microwave and p2be the true proportions of crackers like these that would break if not microwaved. Check if the conditions for calculating a confidence interval forp1-p2met.

Short Answer

Expert verified

It is not suitable to find confidence interval forp1-p2

Step by step solution

01

Given Information

It is given that n1=65

x1=0

n2=65

x2=16

02

Explanation

Testing three conditions for hypothesis test:

Random: As they are assigned, it is satisfied.

Independent: Since all data values in population and used sample, this condition is satisfied.

Normal: There are zero success in first sample, it is not at least 10.

As normal condition is not met, we cannot find confidence intervalp1-p2

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Most popular questions from this chapter

Starting in the 1970s, medical technology has enabled babies with very low birth weight (VLBW, less than1500grams, or about 3.3 pounds) to survive without major handicaps. It was noticed that these children nonetheless had difficulties in school and as adults. A long-term study has followed 242 randomly selected VLBW babies to age 20years, along with a control group of 233 randomly selected babies from the same population who had normal birth weight. 50

a. Is this an experiment or an observational study? Why?

b. At age20,179 of the VLBW group and 193 of the control group had graduated from high school. Do these data provide convincing evidence at the α=0.05 significance level that the graduation rate among VLBW babies is less than for normal-birth-weight babies?

A survey asked a random sample of U.S. adults about their political party affiliation and how long they thought they would survive compared to most people in their community if an apocalyptic disaster were to strike. The responses are summarized in the following two-way table.

Suppose we select one of the survey respondents at random. Which of the following probabilities is the largest?

a. P(Independent and Longer)

b. P(Independent or Not as long)

c. P(Democrat 3051526=0.200=20.0%| Not as long)

d. P(About as long 3051526=0.200=20.0%| Democrat)

e. P(About as long)

Literacy Refer to Exercise 2.

a. Find the probability that the proportion of graduates who pass the test is at most 0.20higher than the proportion of dropouts who pass, assuming that the researcher’s report is correct.

b. Suppose that the difference (Graduate – Dropout) in the sample proportions who pass the test is exactly 0.20. Based on your result in part (a), would this give you reason to doubt the researcher’s claim? Explain your reasoning.

A researcher wished to compare the average amount of time spent in extracurricular activities by high school students in a suburban school district with that in a school district of a large city. The researcher obtained an SRS of 60high school students in a large suburban school district and found the mean time spent in extracurricular activities per week to be 6hours with a standard deviation of 3hours. The researcher also obtained an independent SRS of 40high school students in a large city school district and found the mean time spent in extracurricular activities per week to be 5hours with a standard deviation of 2hours. Suppose that the researcher decides to carry out a significance test of H0: μsuburban=μcity versus a two-sided alternativ

The P-value for the test is 0.048. A correct conclusion is to

a. fail to reject H0because0.048<α=0.05. There is convincing evidence of a difference in the average time spent on extracurricular activities by students in the suburban and city school districts.

b. fail to reject H0because 0.048<α=0.05. There is not convincing evidence of a difference in the average time spent on extracurricular activities by students in the suburban and city school districts.

c. fail to reject H0because0.048<α=0.05. There is convincing evidence that the average time spent on extracurricular activities by students in the suburban and city school districts is the same.

d. reject H0because 0.048<α=0.05. There is not convincing evidence of a difference in the average time spent on extracurricular activities by students in the suburban and city school districts.

e. reject H0because 0.048<α=0.05 . There is convincing evidence of a difference in the average time spent on extracurricular activities by students in the suburban and city school districts.

A quiz question gives random samples of n=10observations from each of two Normally distributed populations. Tom uses a table of t distribution critical values and 9degrees of freedom to calculate a 95%confidence interval for the difference in the two population means. Janelle uses her calculator's two-sample t Interval with 16.87degrees of freedom to compute the 95%confidence interval. Assume that both students calculate the intervals correctly. Which of the following is true?

(a) Tom's confidence interval is wider.

(b) Janelle's confidence Interval is wider.

(c) Both confidence Intervals are the same.

(d) There is insufficient information to determine which confidence interval is wider.

(e) Janelle made a mistake, degrees of freedom has to be a whole number.
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