Question

A manufacturer receives an order for fluorescent light bulbs. The order requires that the bulbs have a mean life span of 950 hours. The manufacturer selects a random sample of 25 fluorescent light bulbs and finds that they have a mean life span of 945 hours with a standard deviation of 15 hours. Test to see if the manufacturer is making acceptable light bulbs. Use a 95% confidence level. Assume the data are normally distributed.

Answer 1

Null hypothesis: H₀ >= 950 hours

Alternate hypothesis: H_a < 950 hours

We know that the sample mean, xbar= 945 hours

Sample standard deviation, s= 15 hours

Since the population standard deviation is not known, and the sample size is less than 30, we will use a t-distribution to build the hypothesis.

critical t score_{24, 0.05} = - 1.711

Thus, if the t statistic is less than -1.7, we will reject the null hypothesis.

t-statistic= (xbar-mu) / s/sqrt(n)

= (945-950) / 15/ sqrt(25)

= -5/ 15/5

= -5/3

= -1.67

Since this value is greater than -1.7, we fail to reject (or accept) the null hypothesis.