A consumer electronics company is comparing the brightness of two different type

Question

A consumer electronics company is comparing the brightness of two different types of picture tubes for use in its television sets. Tube type A has mean brightness of 100 and standard deviation of 16, and tube type B has unknown mean brightness, but the standard deviation is assumed to be identical to that for type A. A random sample of n = 25 tubes of each type is selected, and X_B - X_A is computed. If mu_B equals or exceeds mu_A, the manufacturer would like to adopt type B for use. The observed difference is x_B - x_A = 3.5. What decision would you make, and why?

Explanation / Answer

Solution:

Here, we have to use the two sample t test for the population mean assuming equal population variances.

We have to test

H0: µb µa versus Ha: µb < µa

We are given Xbar(b) – Xbar(a) = 3.5

Test statistic = t = [Xbar(b) – Xbar(a)] / SE

SE = sqrt[(S1^2/N1)+(S2^2/N2)]

SE = sqrt[(16^2/25)+(16^2/25)]

SE = 4.5255

Test statistic = t = 3.5/4.5255 = 0.7734

Degrees of freedom = 24 + 24 = 48

P-value = 0.2215

P-value is greater than alpha value 0.05, so we do not reject the null hypothesis. So, we concluded that manufacturer would adopt type B for use.

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