Question

An analyst wants to test a hypothesis on the means of two populations. She takes samples from each population. The variances of the population are not known, but are assumed to be equal. Statistics calculated from these samples are

Sample 1                                          

Average 1,053.6

Count 34

Sample 2                                          

Average 1,079

Count 29

The pooled variance is calculated as 365.9 Based on this data calculate the t statistic to use in the hypothesis test. Enter your answer to 2 decimal places.

Answer 1

Solution

Given ,

$url=https://latex.codecogs.com/gif.latex?%5Cbar%20x_%7B1%7D&t=1572923763&ymreqid=50870fb5-0ab3-84d7-1c7d-410067016800&sig=D.hguB0Vyc.wFDG4_TkLng--~C$  = 1053.6 $url=https://latex.codecogs.com/gif.latex?%5Cbar%20x_%7B2%7D&t=1572923763&ymreqid=50870fb5-0ab3-84d7-1c7d-410067016800&sig=dU94KkP8fDAnSlLiZ.8zMw--~C$ = 1079

n₁ = 34 n₂ = 29

The pooled variance is calculated as 365.9

i.e.   $url=https://latex.codecogs.com/gif.latex?s_%7Bp%7D%5E%7B2%7D&t=1572923763&ymreqid=50870fb5-0ab3-84d7-1c7d-410067016800&sig=P_FTK4t6eLqi2bMOTPxj9w--~C$ =   365.9

The test statistic t is given by

t = $url=https://latex.codecogs.com/gif.latex?%5Cfrac%7B%5Cbar%20x_%7B1%7D-%5Cbar%20x_%7B2%7D%7D%7B%5Csqrt%7Bs_%7Bp%7D%5E%7B2%7D%28%5Cfrac%7B1%7D%7Bn_%7B1%7D%7D+%5Cfrac%7B1%7D%7Bn_%7B2%7D%7D%29%7D%7D&t=1572923763&ymreqid=50870fb5-0ab3-84d7-1c7d-410067016800&sig=2rM3X2BMg9_P661L46.nLw--~C$

= $\frac{1053.6 - 1079}{\sqrt{365.9(\frac{1}{34}+\frac{1}{29})}}$

=  -5.25316079756

= -5.25

The t statistic to use in the hypothesis test = -5.25