Please show formulas 1 ToysRUs and the Teddy Bear stores cla

Please show formulas:

1. ToysRUs and the Teddy Bear stores claimed that their toys last longer.
Which store toys last longer? Test at .05 significance level

ToysRUs: Average toy life= 14.50 years; standard deviation = 1.50 years; n = 10

TeddyBear store claimed: Average toy life = 13.60 years; standard deviation = 2.10 years; n = 11

2. Another text done by the human resources was about how long different categories of
employees are working (hours /pay period).
Who works longer, married or unmarried employees? Test at a =.01
Unmarried Employee Married Employee
X1 = 78.5 hours X2 = 77 hours
s1 = 14.0 hours S2 = 16.0 hours
N1 = 140 N2 = 160

Solution

Ans1.

Here, the hypotheses can be formulated as:

Let 1 be the population mean of the ToysRus and 2 be that for TeddyBear.

H0: 1= 2

H1: 1 2

Then SE= sqrt[(s₁²/n₁) + (s₂²/n₂)] = sqrt[ 1.5*1.5/10 + 2.1*2.1/11] = sqrt(0.225+0.4)= sqrt 0.625 = 0.79

Then, DF = (s₁²/n₁ + s₂²/n₂)² / { [ (s₁² / n₁)² / (n₁ - 1) ] + [ (s₂² / n₂)² / (n₂ - 1) ] }

= (0.225+0.4)^2 / { 0.005625+0.016}

= 0.390625/0.021625= 18.063

T= 14.5-13.6/0.79= 1.139

The value of the t statistic from the table at the given level of significance is 1.734

As the calculated value is less than the tabulated value, we conclude that we do not reject the null hypothesis that both the stores have equal average toy life.