Question

Company A = mean 1300
= Standard deviation 82
.= Sample number 100
Company B= mean 1248
.... = Standard deviation 93
= Sample number 100
Which brand of bulbs are you going to buy if you wish to take risk at 5%

Answer 1

Company A

$n_1=100 \\ \bar{x}_1 = 1300 \\ s_1=80$

Company B

$n_2=100 \\ \bar{x}_2=1248 \\ s_2=93 \\ H_0: \mu_1= \mu_2 \\ H_1: \mu_1 ≠ \mu_2$

Test-statistic: two-sample t test

$t = \frac{\bar{x_1} -\bar{x_2}}{s_p \sqrt{ \frac{1}{n_1} + \frac{1}{n_2} }} \\ s^2_p= \frac{(n_1-1)s^2_1 + (n_2-1)s^2_2}{n_1+n_2-2} \\ s^2_p = \frac{(100-1) \times (80)^2 + (100-1) \times (93)^2}{100+100-2} \\ = \frac{633600+856251}{198} \\ = 7524.5 \\ s_p= \sqrt{7524.5}=86.74 \\ t = \frac{1300 -1248}{86.74 \sqrt{ \frac{1}{100} + \frac{1}{100} }} \\ = \frac{52}{12.26} \\ = 4.24$

Tabulated value of t at 5% level of significance and d.f.= 100 +100 – 2 = 198 is 1.972.

Since the calculated value of t is greater than the tabulated value of t at 5% level of significance, H₀ is rejected. There is a significant difference in the mean life of bulbs of the two companies.

I am going to buy bulbs of brand A.