Statistics for People Who (Think They) Hate Statistics
Statistics for People Who (Think They) Hate Statistics
6th Edition
ISBN: 9781506333830
Author: Neil J. Salkind
Publisher: SAGE Publications, Inc
Question
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Chapter 11, Problem 1TP
To determine

To test: The research hypothesis at the .05 level of significance that boys raise their hand in class more often than girls and decide whether this is a one-or two-tailed test.

Expert Solution & Answer
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Answer to Problem 1TP

The research hypothesis is one tailed (right) test because the number of hands raised by boys is greater than girls. Boys raise their hands significantly more.

Explanation of Solution

Calculation:

The given data is represents the gender and hand up wise in which 1=”Boys” and 2=”Girls”.

GenderHand UpGenderHand Up
1918
2327
2519
2129
1818
1427
2223
2627
1926
13110
2417
1816
23112
11028
2628

The claim is,

The null hypothesis is as follows:

H0: Hands raised by boys and girls are equal.

The alternative hypothesis is as follows:

H1: Hands raise by boys are more than girls.

The t-test for difference of mean is given by:

t=X1¯X¯2(n1+n2n1n2×1n1+n22[(n11)s12+(n21)s22])t(n1+n22) (1)

s12=1n11(XX¯)

s22=1n21(YY¯)

X¯=1n1X and Y¯=1n2Y

Where,

  • n1 is the sample size of boys.
  • n2 is the sample size of girls.
  • s12 is the sample variance of boys.
  • s22 is the sample variance of girls.
  • X1¯ is the mean of boys sample.
  • X2¯ is the mean of girls sample.

The value of (XX¯)2 is tabulated below:

BoysHands Up (X)(XX¯)2
191.147959184
180.005102041
1415.43367347
191.147959184
1324.29081633
180.005102041
1104.290816327
180.005102041
191.147959184
180.005102041
1104.290816327
170.862244898
163.719387755
11216.57653061
Total11172.92857143

Substitute 111 for X and 72.928 for (XX¯)2 in above X¯ and s12 formula.

X¯=11114=7.92

And,

s12=72.9213=5.60

Similarly for the girls:

GirlsHands Up (Y)(YY¯)2
235.34765625
250.09765625
2118.59765625
2210.97265625
260.47265625
241.72265625
235.34765625
260.47265625
272.84765625
2913.59765625
272.84765625
235.34765625
272.84765625
260.47265625
287.22265625
287.22265625
Total8585.4375

Substitute 85 for Y and 85.437 for (YY¯)2  in above Y¯ and s22 formula.

Y¯=8516=5.31

And,

s22=85.4315=5.96

Substitute 7.92 for X¯, 5.60 for s12, 5.31 for Y¯, 5.96 for s22, 14 for n1 and 16 for n2 in equation (1).

t=7.925.31(14+1614×16×114+162[(141)×5.60+(161)5.69])=2.610.7564=2.610.8697=3.001

The critical value at 28 d.f and 5% level of significance is 1.701.

The calculated t value is 3.001, which is greater than tabulated value (1.701) at 5% level of significance. Hence, the null hypothesis is rejected. Therefore, hands raised by boys are more than girls. The research hypothesis is one tailed (right) test because the number of hands raised by boys is greater than girls.

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