Hypothesis Testing

Question

Hypothesis Testing

A company manufactures car batteries with an average life span of 2 years or more. An engineer believes that that this value is less than that claimed by the company. Using 10 samples, he measures the average life span to be 1.8 years with a standard deviation of 0.15.

1.     State the Null and Alternate hypothesis.

2.     At 99% confidence level, is there enough evidence to discard the Null hypothesis?

Answer 1

Hypothesis Testing

A company manufactures car batteries with an average life span of 2 years or more. An engineer believes that that this value is less than that claimed by the company. Using 10 samples, he measures the average life span to be 1.8 years with a standard deviation of 0.15.

1.     State the Null and Alternate hypothesis.

2.     At 99% confidence level, is there enough evidence to discard the Null hypothesis?

Answers:

Part-1

H₀: mu >= 2 (mu₀)

Ha: mu <2

This is a one tailed test.

Part-2

             Confidence level: 99%. Hence, significance level = 0.01

             Sample size n=10

             Since n<30 and population standard deviation is not known, we apply t-test.

             Degree of freedom df = n-1 = 10-1 = 9

             At a cumulative probability of t_.99 and df = 9, we get t_c = 2.821 (from t-table)

             Since we are dealing with a left hand t test (mu <2), t_c = -2.821

             

Part-3

             x-bar = 1.8

             s = 0.15             

From the data,

t = (x-bar - mu₀)/(s/SQRT(n)) = (1.8 – 2)/(0.15/SQRT(10))

t = (-0.2)/(0.15 * 3.1623) = -0.2/0.47434 = -4.22 (rounded to 2 decimal places)

The t value of -4.22 < -2.281 , the latter being the critical value.

Hence, the data t falls in the rejection region.

Therefore, At 99% confidence level, there is enough evidence to discard the Null hypothesis.