Determine whether the sampling method described below appears to be sound or is flawed.

In a survey of 655 human resource​ professionals, each was asked about the importance of the education of a job applicant. The survey subjects were randomly selected by pollsters from a reputable market research firm.

It appears to be sound because the data are not biased in any way.

Determine whether the results below appear to have statistical​ significance, and also determine whether the results have practical significance.

In a study of a weight loss​ program, 5 subjects lost an average of 43 lbs. It is found that there is about a 21​% chance of getting such results with a diet that has no effect.

No, the program is not statistically significant because the results are likely to occur by chance.

Yes, the program is practically significant because the amount of lost weight is large enough to be considered practically significant.

In a study of a weight loss​ program, 40 subjects lost a mean of 3.5 lbs after 12 months. Methods of statistics can be used to show that if this diet had no​ effect, the likelihood of getting these results is roughly 10 chances in 1000. Does the weight loss program have statistical​ significance? Does the weight loss program have practical​ significance?

Yes, the program is statistically significant because the results are unlikely to occur by chance.

​No, the program is not practically significant because someone starting a weight loss program would likely want to lose considerably more than 3.5 lb.

The data in table 1 are the weights​ (in kilograms) of freshman students. The​ x-values are weights measured in September and the​ y-values are their corresponding weights measured in April of the following spring. The​ x-values in table 2 are nicotine amounts​ (in mg) in different 100 mm​ filtered, non-"light" menthol cigarettes. The​ y-values in table 2 are nicotine amounts​ (in mg) in different​ king-size nonfiltered,​ nonmenthol, and​ non-"light" cigarettes.

In data table​ 2, is each​ x-value matched with a corresponding​ y-value, as in data table​ 1? That​ is, is each​ x-value associated with the corresponding​ y-value in some meaningful​ way?

In table​ 2, does it make sense to use the difference between each​ x-value and the​ y-value that is in the same​ column?

No​ because, unlike table 1 in which each weight in September is matched with the weight of the same student in​ April, there is no association between the cigarettes. The order of the​ x-values does not correspond in any way with the order of the​ y-values.

No because none of the​ x-values are associated with any of the​ y-values. Since they are not​ associated, the differences between the​ x- and​ y-values have no real meaning.

Given the data in the table​ below, what issue can be addressed by conducting a statistical analysis of the pulse​ rates?

Statistical analysis involves the ability to see the big​ picture; to consider such relevant factors as​ context, source of​ data, and sampling​ method; and to form conclusions and identify practical implications. Statistical analysis involves critical thinking and the ability to make sense of results. In this​ case, the data can be used to address the issue of whether males or females have pulse rates with the same average​ (mean) values since one could compute the average pulse rate of the five males and five females.

Refer to the given table of measurements below.

Is there some meaningful way in which the IQ scores are matched with the corresponding brain​ volumes?

If they are​ matched, does it make sense to use the difference between each IQ score and brain volume that is in the same​ column? Why or why​ not?

​Yes, each IQ score is matched with the brain volume in the same​ column, because they are measurements obtained from the same person.

No, it does not make sense to use the difference between each IQ score and brain volume in the same​ column, because IQ scores and brain volumes use different units of measurement.

In the data table​ below, the​ x-values are the weights​ (in pounds) of cars and the​ y-values are the corresponding highway fuel consumption amounts​ (in mi/gal).

Comment on the source of the data if you are told that car manufacturers supplied the values. Is there an incentive for car manufacturers to report values that are not​ accurate?

Yes, because​ consumers, in​ general, would prefer to buy a car with a higher level of fuel efficiency. In this​ case, the source of the data would be suspect with a potential for bias.

Several studies showed that after eating a very large meal​, subjects had increased risk of heart attack. A diet food manufacturer financed this research. What is wrong with this​ study?

Self-interest study

Based on a study of ages of men and women who have children​, a researcher concludes that being a parent causes people to age. Do you agree with this​ conclusion?

No. There may be a relationship between having children and the age of an adult​, but that does not mean that one causes the other.

A polling company reported that 57​% of 1018 surveyed adults said that rising gas prices are "quite annoying." Complete parts​ (a) through​ (d) below.

a. What is the exact value that is 57​% of 1018​?

b. Could the result from part​ (a) be the actual number of adults who said that rising gas prices are "quite annoying" question mark Why or why​ not?

c. What could be the actual number of adults who said that rising gas prices are "quite annoying"?

d. Among the 1018 ​respondents, 128 said that rising gas prices are "not at all annoying." What percentage of respondents said that rising gas prices are "not at all annoying"?

a. The exact value is 580.26.

b. No, the result from part​ (a) could not be the actual number of adults who said that rising gas prices are "quite annoying" because a count of people must result in a whole number.

c. The actual number of adults with this opinion could be 581.

d. 12.57​%

A polling company reported that 59​% of 2302 surveyed adults said that they play baseball. Complete parts​ (a) through​ (d) below.

a. What is the exact value that is 59​% of 2302​?

b. Could the result from part​ (a) be the actual number of adults who said that they play baseball question mark Why or why​ not?

c. What could be the actual number of adults who said that they play baseball?

d. Among the 2302 ​​respondents, 765 said that they only play hockey. What percentage of respondents said that they only play​ hockey?

a. The exact value is 1358.18.

b. ​No, the result from part​ (a) could not be the actual number of adults who said that they play baseball because a count of people must result in a whole number.

c. The actual number of adults who play baseball could be 1359.

d. 33.23​%

A report about the decline of Western investment in third world countries included this: "After years of daily flights, several European airlines halted passenger service. Foreign investment fell 400 percent during the 1990s. What is wrong with this​ statement?

If foreign investment fell by 100%, it would be totally eliminated, so it not possible for it to fall by more than 100%.

A researcher was once criticized for falsifying data. Among his data were figures obtained from 8 groups of mice​, with 5 individual mice in each group. These values were given for the percentage of successes in each​ group: 53%,​ 58%, 63%, ​46%, 48% , 67% , 54% , 42%. ​What's wrong with those​ values?

All percentages of success should be multiples of 20. The given percentages cannot be correct.

A researcher was once criticized for falsifying data. Among his data were figures obtained from 8 groups of mice​, with 5 individual mice in each group. These values were given for the percentage of successes in each​ group: 53%,​ 58%, 63%, ​46%, 48% , 67% . ​What's wrong with those​ values?

All percentages of success should be multiples of 25. The given percentages cannot be correct.

Which of the following is typically the least important factor to consider when conducting a statistical analysis of​ data?

Formula calculation

In learning to think​ statistically, common sense and practical considerations are typically more important than calculations and formulas.

Which of the following is NOT a voluntary response​ sample?

Quiz scores from a college level statistics course are analyzed to determine student progress.

Using quiz scores from a college level statistics course that are analyzed to determine student progress would not be a voluntary response sample because respondents themselves do not decide to be included.

What does it mean for the findings of a statistical analysis of data to be statistically​ significant?

The likelihood of getting these results by chance is very small.

Statistical significance is indicated when methods of statistics are used to reach a conclusion that it is unlikely that the findings occurred by chance.

Which of the following would be considered practically​ significant?

In a very large​ study, it was found that Treatment I resulted in​ 93% success while Treatment II resulted in​ 75% success.

A very large study in which it was found that Treatment I resulted in​ 93% success while Treatment II resulted in​ 75% success is practically significant since Treatment I appears to have a substantially higher success rate.

What is the goal of learning​ statistics?

To learn to distinguish between statistical conclusions that are likely to be valid and those that are seriously flawed

Statistics is the science of planning studies and​ experiments, obtaining​ data, and then​ organizing, summarizing,​ presenting, analyzing,​ interpreting, and drawing conclusions based on the data. Statisticians universally agree that statistical thinking is​ good, but there are different views of what actually constitutes statistical thinking. Statistical thinking involves critical thinking and the ability to make sense of results. Statistical thinking might involve determining whether results are statistically significant.

Which of the following would NOT cast doubt of the usefulness of sample​ data?

An effective sampling method

In the use of​ statistics, effective sampling methods are important. If sample data are not collected in an appropriate​ way, the data may be useless.

What is a​ self-interest study?

A survey in which the sponsor can enjoy monetary or other gains from the results

A​ self-interest study is a survey in which the sponsor can enjoy monetary or other gains from the results. Be very wary of studies where the sponsor has certain interests to promote.