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“Sectoring by Industry Groups.” Nasdaq. Available online at http://www.nasdaq.com/markets/barchart-sectors.aspx?page=sectors&base=industry (accessed June 17, 2013).

“Strip Clubs: Where Prostitution and Trafficking Happen.” Prostitution Research and Education, 2013. Available online at www.prostitutionresearch.com/ProsViolPosttrauStress.html (accessed June 17, 2013).

“World Series History.” Baseball-Almanac, 2013. Available online at http://www.baseball-almanac.com/ws/wsmenu.shtml (accessed June 17, 2013).

Chapter review

Two population means from independent samples where the population standard deviations are not known

  • Random Variable: X ¯ 1 X ¯ 2 = the difference of the sampling means
  • Distribution: Student's t -distribution with degrees of freedom (variances not pooled)

Formula review

Standard error: SE = ( s 1 ) 2 n 1 + ( s 2 ) 2 n 2

Test statistic ( t -score): t = ( x ¯ 1 x ¯ 2 ) ( μ 1 μ 2 ) ( s 1 ) 2 n 1 + ( s 2 ) 2 n 2

Degrees of freedom:
d f =   ( ( s 1 ) 2 n 1 +   ( s 2 ) 2 n 2 ) 2 ( 1 n 1 1 ) ( ( s 1 ) 2 n 1 ) 2 + ( 1 n 2 1 ) ( ( s 2 ) 2 n 2 ) 2

where:

s 1 and s 2 are the sample standard deviations, and n 1 and n 2 are the sample sizes.

x ¯ 1 and x ¯ 2 are the sample means.

Cohen’s d is the measure of effect size:

d = x ¯ 1 x ¯ 2 s p o o l e d
where s p o o l e d = ( n 1 1 ) s 1 2 + ( n 2 1 ) s 2 2 n 1 + n 2 2

Use the following information to answer the next 15 exercises: Indicate if the hypothesis test is for

  1. independent group means, population standard deviations, and/or variances known
  2. independent group means, population standard deviations, and/or variances unknown
  3. matched or paired samples
  4. single mean
  5. two proportions
  6. single proportion

It is believed that 70% of males pass their drivers test in the first attempt, while 65% of females pass the test in the first attempt. Of interest is whether the proportions are in fact equal.

two proportions

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A new laundry detergent is tested on consumers. Of interest is the proportion of consumers who prefer the new brand over the leading competitor. A study is done to test this.

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A new windshield treatment claims to repel water more effectively. Ten windshields are tested by simulating rain without the new treatment. The same windshields are then treated, and the experiment is run again. A hypothesis test is conducted.

matched or paired samples

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The known standard deviation in salary for all mid-level professionals in the financial industry is $11,000. Company A and Company B are in the financial industry. Suppose samples are taken of mid-level professionals from Company A and from Company B. The sample mean salary for mid-level professionals in Company A is $80,000. The sample mean salary for mid-level professionals in Company B is $96,000. Company A and Company B management want to know if their mid-level professionals are paid differently, on average.

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The average worker in Germany gets eight weeks of paid vacation.

single mean

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According to a television commercial, 80% of dentists agree that Ultrafresh toothpaste is the best on the market.

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It is believed that the average grade on an English essay in a particular school system for females is higher than for males. A random sample of 31 females had a mean score of 82 with a standard deviation of three, and a random sample of 25 males had a mean score of 76 with a standard deviation of four.

independent group means, population standard deviations and/or variances unknown

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Source:  OpenStax, Introductory statistics. OpenStax CNX. May 06, 2016 Download for free at http://legacy.cnx.org/content/col11562/1.18
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