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The candy machine Suppose a large candy machine has 45%orange candies, Use Figures 7.11and7.12(page 434) to help answer the following questions.

(a) Would you be surprised if a sample of 25candies from the machine contained 8orange candies (that's 32%orange)? How about 5orange candies ( 20%orange)? Explain.

(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.

Short Answer

Expert verified

(a) Obtaining 8orange candies is not very surprising,

Obtaining 5orange candies is surprising.

(b) Getting a sample of 50candies in which 32%are orange candies is more surprising.

Step by step solution

01

Part (a) Step 1: Given Information 

Given in the question that sample of 25candies from the machine contained 8orange candies (that's 32%orange)? and 5orange candies ( 20%orange).we have to find that which sample would be surprised.

02

Part (a) Step 2: Explanation 

In the candy machine, the percentage of orange candies is 45

The dot plot shows that the sample percentage of 32percent has a lot of dots above it, indicating that getting a sample proportion of 32percent is quite likely.

As a result, getting 8orange candies isn't all that surprising.

In the dot plot, the sample percentage of 20% now has no dots above it, indicating that getting a sample proportion of 20%is unlikely.

As a result, getting5 orange candy is a pleasant surprise.

03

Part (b) Step 1: Given Information 

Given in the question that a sample of 25candies in which 32%are orange or getting a sample of 50candies in which 32%are orange we have to find Which is more surprising.

04

Part (b) Step 2:  Explanation 

In the candy machine, the percentage of orange candies is 45%

In the dot plots, the centre of the distribution is around 0.45.

It can be seen that the population proportion of 0.45is not very close to32%

It is more unusual to achieve a sample proportion that differs from the population proportion for a sample with a greater sample size.

As a result, receiving a sampling of 50candies, with 32percent of them being orange candies, is even more shocking.

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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≤0.65-0.71(0.71)(0.29)100)Pz≤0.65-0.71(0.71)(0.29)100

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

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

A statistic is an unbiased estimator of a parameter when

a. the statistic is calculated from a random sample.

b. in a single sample, the value of the statistic is equal to the value of the parameter.

c. in many samples, the values of the statistic are very close to the value of the

parameter.

d. in many samples, the values of the statistic are centered at the value of the parameter.

e. in many samples, the distribution of the statistic has a shape that is approximately

Normal.

Bad eggs Selling eggs that are contaminated with salmonella can cause food poisoning in consumers. A large egg producer randomly selects 200 eggs from all the eggs shipped in one day. The laboratory reports that 9 of these eggs had salmonella contamination. Identify the population, the parameter, the sample, and the statistic.

Which of the following statements about the sampling distribution of the sample mean is incorrect?

a. The standard deviation of the sampling distribution will decrease as the sample size increases.

b. The standard deviation of the sampling distribution measures how far the sample mean typically varies from the population mean.

c. The sample mean is an unbiased estimator of the population mean.

d. The sampling distribution shows how the sample mean is distributed around the population mean.

e. The sampling distribution shows how the sample is distributed around the sample mean.

The manufacturer of a certain brand of aluminum foil claims that the amount of foil on each roll follows a Normal distribution with a mean of 250 square feet (ft2 ) and a standard deviation of 2 ft2 . To test this claim, a restaurant randomly selects 10 rolls of this aluminum foil and carefully measures the mean area to bex=249.6ft2.

a. Find the probability that the sample mean area is 249.6ft2or less if the manufacturer’s claim is true.

b. Based on your answer to part (a), is there convincing evidence that the company is overstating the average area of its aluminum foil rolls?

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