A new light bulb is being considered for use in an office wi

A new light bulb is being considered for use in an office with computers. It is decided that the new bulb will only be used if it has a mean lifetime of more than 500 hours. A random sample of 40 bulbs is selected and placed on life test. The mean and standard deviation are found to be 505 hours and 18 hours, respectively. Perform the appropriate test of hypothesis to determine whether the new bulb should be used. Use a 0.01 level of significance. A. 1 tailed right B. 1 tailed left C. 0 tailed D. 2 tailed

Solution

Null Hyp: H₀: mu = 500

Alt Hyp: Ha: mu > 500

The test is 1 tailed right

Sample size n = 40; sample mean xbar = 505 sample stdev = 18

Test statistic t = (xbar - mean)/(stdev/sqrt(n))

= (505 - 500)/(18/sqrt(40))

= 1.75

Critical value of t for 0.01 sig level and degrees of freedom (n - 1 = 39) is 2.425

Rejection region is t > 2.425

Since the test statistic is < critical value we fail to reject the Null and conclude that there is not enough evidence to support the claim that the mean lifetime is more than 500 hours.