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Chapter 7: Q. 15 (page 455)

Suppose that the sample proportion of students who did all their assigned homework last week is p^=57100=0.57. Would this sample proportion provide convincing evidence that less than 60%of all students at the school completed all their assigned homework last week? Explain your reasoning.

Short Answer

Expert verified

A sample proportion of p^鈮�0.57happened 78250=31.27%of the time, so it would not be surprising to get p^鈮�0.57. Since it is not surprising, it does not provide convincing evidence.

Step by step solution

01

Given information

We have been given that the sample proportion of students who did all their assigned homework last week is p^=57100=0.57

02

Explanation

The sample proportion (p^) refers to the percentage of people in a sample who have a particular attribute or trait. The sample proportion is the percentage of successful samples; to calculate it, divide the number of people (or objects) who have the desired feature by the total number of persons (or items) in the sample.

Because 78250=31.27%, of the values of p^in the simulation are less than or equal to 0.57, a sample fraction of p^=0.57or less in an SRS of size 100from a population with p =0.60 would not be surprising. A sample proportion of p^鈮�0.57does not provide convincing evidence that the population proportion of students who completed all of their assigned homework is less than p^=60%.

The disparity between the observed proportion (p^=0.57) and the proportion stated (p =0.60) could be explained by sampling variability.

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Most popular questions from this chapter

According to the U.S. Census, the proportion of adults in a certain county who owned their own home was 0.71. An SRS of 100 adults in a certain section of the county found that 65 owned their home. Which one of the following represents the approximate probability of obtaining a sample of 100 adults in which 65 or fewer own their home, assuming that this section of the county has the same overall proportion of adults who own their home as does the entire county?

a. (10065)(0.71)65(0.29)3510065(0.71)65(0.29)35

b. (10065)(0.29)65(0.71)3510065(0.29)65(0.71)35

c.

P(z鈮�0.65-0.71(0.71)(0.29)100)Pz鈮�0.65-0.71(0.71)(0.29)100

d.P(z鈮�0.65-0.71(0.65)(0.35)100)Pz鈮�0.65-0.71(0.65)(0.35)100

e.P(z鈮�0.65-0.71(0.71)(0.29)100)Pz鈮�0.65-0.71(0.71)(0.29)100

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a. Make a bar graph of the population distribution.

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(b) Which is more surprising getting a sample of 25candies in which 32%are orange or getting a sample of 50candies in which 32%are orange? Explain.

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