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Bob has a bulb factory that produces white light bulbs. He sold some bulbs to Peter claiming that on average the service life of his bulbs is at least 980 hours. To test this claim Peter gathered information on the 20 bulbs purchased. He found that the mean service life is 960 and knows that the variance of service life for the population is . Which of the following statements properly analyzes Bob’s claim? Assume that the distribution service life of bulbs is normal.
a. Using a t-test you conclude that both types of bulbs have different mean service life at the 5% level.
b. Using a t-test you conclude that both types of bulbs have the same mean service life at the 5% level.
c. Using a z-test you conclude that both types of bulbs have the same mean service life at the 5% level.
d. Using a t-test you conclude that both types of bulbs have the same mean service life at the 1% level.
e. Using a z-test you conclude that both types of bulbs have different mean service life at the 5% level.

Answer :

akiran007

Answer:

a. Using a t-test you conclude that both types of bulbs have different mean service life at the 5% level.

Step-by-step explanation:

The t test will be used as

1) the sample size is less than 30

2) the population standard deviation is knows and is s= √200= 14.142

Using the test statistic

t= x- u/ s/ √n

t= 960-980/ 14.142/ √20

t= -0.316

It is one tailed test as the claim is

H0: u ≥ 980 and the alternate hypothesis is Ha : u< 980

The  critical region for one tailed test with n-1 = 20-1 = 19 degrees of freedom  is t < 1.729 for ∝= 0.05

The  critical region for one tailed test with n-1 = 20-1 = 19 degrees of freedom  is t < 2.539 for ∝= 0.01

Since the calculated value of t= -0.136  falls in the critical region we conclude that the null hypothesis is false and the average life of the bulbs is less than 980. We accept the alternate hypothesis.

Only choice a is correct.

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