Question

Four golfers are asked to play a round of golf each on two consecutive Saturday afternoons. During the first round, one of two club types is to be used. During the second round, another club type is to be used. The order in which a golfer uses each brand is determined randomly. Scores are recorded. The results are given below.

Golfer Brand 1 Brand 2
1 93 95
2 88 86
3 112 111
4 79 77

To determine if the mean scores differ by brand of club, we would use

a. the one-sample t test.
b. matched pairs t test.
c. two-sample t test.
d. Any of the above are valid. It is at the experimenter's discretion.

Answer 1

Answer:

c) Two sample t-test

Step-by-step explanation:

Given data

Golfer                          1             2                  3               4

Brand1 (x)                  93          88                112            79

Brand 2 (y)               95          86                 111            77

 

Mean of x =

                  $\frac{93+88+112+79}{4} = 93$

            x⁻ = 93

Mean of y

                $\frac{95+86+111+77}{4} = 92.25$

            y ⁻ = 92.25

Given data

Brand1 (x)         :         93            88                112            79

Brand 2 (y)       :        95             86                111             77

x- x⁻                 :        0                -5                19              -14

y -y ⁻                 :        2.75         -6.25           18.75        -15.25

(x- x⁻)²              :         0                 25             361            196

( y -y ⁻  )²         :       7.5625      39.0625      351.5625    232.5625

S² =     $\frac{sum((x- x^{-} )^{2} +sum (y- y^{-} )^{2} }{n_{1}+n_{2} -2 }$

$S^{2} = \frac{582+630.75}{4+4-2} = 202.125$

S = 14.21706

 

Null hypothesis: H₀: There is no significant difference between the means

Alternative hypothesis: H₁: There is significant difference between the means

Student's t test for difference for means

The test statistic

$t = \frac{x^{-} -y^{-} }{\sqrt{S^{2}(\frac{1}{n_{1} } +\frac{1}{n_{2} } } }$

$t = \frac{93 -92.25}{\sqrt{202.125(\frac{1}{4 } +\frac{1}{4 } } }$

on calculation , we get

t = 0.0746

Degrees of freedom ν = n₁ +n₂ -2 = 4+4-2 =6

$t_{\frac{\alpha }{2} } = t_{\frac{0.05}{2} } = t_{0.025} = 2.447$

The calculated value t = 0.0746 < 2.447 at 0.05 level of significance

null hypothesis is accepted

Conclusion:-

There is no significant difference between the means