Question

Rakesh claims that LED bulbs manufactured at his factory have mean life of 20 months Random sample of 7 such bulbs gave values 19,21,25,16,17,14,21 Is Rakesh's claim valid at 1% level of Significance. Calculate t test

Answer 1

Answer:

Step 1 : Let µ and σ2 be respectively the mean and the variance of the population under study, where σ2 is known. If µ0 is an admissible value of µ, then frame the null hypothesis as H0: µ = µ0 and choose the suitable alternative hypothesis from

(i) H1: µ ≠ µ0 (ii) H1: µ > µ0 (iii) H1: µ < µ0

Step 2 : Let (X 1, X2 , …, Xn) be a random sample of n observations drawn from the population, where n is large (n ≥ 30).

Step 3 : Let the level of significance be α.

Step 4 : Consider the test statistic under H0. Here, represents the sample mean, which is defined in Note 2. The approximate sampling distribution of the test statistic under H0 is the N(0,1) distribution.

Step 5 : Calculate the value of Z for the given sample (x1, x2, ..., xn) as

Step 6 : Find the critical value, ze, corresponding to α and H1 from the following table

Step 7 : Decide on H0 choosing the suitable rejection rule from the following table corresponding to H1.

Explanation:

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