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Chapter 9: Q 34. (page 567)

Explaining confidence: Here is an explanation from a newspaper concerning one of its opinion polls. Explain what is wrong with the following statement.

For a poll of 1600 adults, the variation due to sampling error is no more than 3

percentage points either way. The error margin is said to be valid at the 95%

confidence level. This means that, if the same questions were repeated in 20 polls, the results of at least 19 surveys would be within 3 percentage points of the results of this survey.

Short Answer

Expert verified

The results do not need to be in same margin of results. "At least" expression is wrong,

Step by step solution

01

Given Information

It is given that:

For a poll of 1600 adults, the variation due to sampling error is no more than 3

percentage points either way. The error margin is said to be valid at the 95%

confidence level. This means that, if the same questions were repeated in 20polls, the results of at least 19surveys would be within 3percentage points of the results of this survey.

02

Explanation

The results of 19among does not need to be in margin of results as it can give results which are not accurate for entire population.

It would have been correct to interpret that 19/20has confidence intervals that contain true population proportion.

Also it is possible that less than 19surveys have true population, it means "at least" is also incorrect.

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Most popular questions from this chapter

The reason we use t procedures instead of z procedures when carrying out a test about a population mean is that

a. z requires that the sample size be large.

b. z requires that you know the population standard deviation 蟽

c. z requires that the data come from a random sample.

d. z requires that the population distribution be Normal.

e. z can only be used for proportions.

Making conclusions A student performs a test of H0:p=0.75versus Ha:p<0.75at 伪=0.05significance level and gets a P-value of 0.22

The student writes: 鈥淏ecause the P-value is large, we accept H0. The data provide convincing evidence that null hypothesis is true". Explain what is wrong with this conclusion.

A random sample of 100 likely voters in a small city produced 59 voters in favor of Candidate A. The observed value of the standardized test statistic for performing a test of H0:p=0.5H0:p=0.5versus Ha:p>0.5Ha:p>0.5

is which of the following?

a)z=0.59-0.50.59(0.41)100

b)z=0.59-0.50.5(0.5)100

c)z=0.5-0.590.59(0.41)100

d)z=0.5-0.590.5(0.5)100

e)z=0.59-0.5100

Powerful potatoes Refer to Exercise 85. Determine if each of the following

changes would increase or decrease the power of the test. Explain your answers.

a. Change the significance level to 伪=0.10

b. Take a random sample of 250 potatoes instead of 500 potatoes.

c. The true proportion is p=0.10 instead of p=0.11

Which of the following is not a condition for performing a significance test about an unknown population proportion p?

(a) The data should come from a random sample or randomized experiment.

(b) Individual measurements should be independent of one another.

(c) The population distribution should be approximately Normal, unless the sample size is large.

(d) Both np and n(1 - p) should be at least 10.

(e) If you are sampling without replacement from a finite population, then you should sample no more than 10% of the population.
See all solutions

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