Question

7. Assume that a simple random sample has been selected from a normally distrib and test the given claim. Use cither the traditional method or P-value method as indicato been selected from a normally distributed population e indicated. Identify the null and alternative hypotheses, test statistic, critical value(s) or P-value (or range of P-values) as appropriate, and state the final conclusion that addresses the original claim. A light-bulb manufacturer advertises that the averace life for its light bulbs is 900 hours. A random sample of 15 of its light bulbs resulted in the following lives in hours. 95 590 510 539 739 917 571 555 916 728 664 693 708 887 849 at the 10% significance level. test the claim that the sample is from a population with a mean life of 900 hours. Use the P-value method of testing hypotheses. (10 points)

Answer 1

The hypothesis to be tested is,

H0 : average life of light bulbs is 900 hours

V/s

H1 : average life of light bulbs is not 900 hours

H0 : null hypothesis

H1 : alternative hypthesis

Test statistic under H0,

t = (sample mean - mean under H0) /(standard deviation/$\sqrt$n)

(we use student's t distribution as sample size is small and population standard deviation is unknown)

Sample mean =$\sum$xi / n

Sample mean = 724.0667

Sample Standard deviation = 156.9242

n=15

Hence test statistic is

t = - 4.34

Critical value is given by,

tn-1,$\alpha$/2 = t14,0.05 = 1.76

P-value = P(| tn-1 | < t)

P-value = P(| t14 | < - 4.34)

P-value = 2 * P(t14 > 4.34)

(since t distribution is symmetric)

P-value = 0.0007

Decision :

P-value < $\alpha$

Hence we reject H0 at 10% level of significance

Conclusion :

The average life of light bulbs may not be 900 hours.