Question

The quality control department has collected data on defective products produced over a 24 hours time span. Using a random sample of 1500 products, they discover that the average number of defects is 254, while the sample standard deviation is 20. The department wants to conduct a test of whether the average number of defective product is equal to 252 or not.

Which of the following is true?

	a.	The Null Hypothesis can be rejected with 95% confidence.
	b.	The Null Hypothesis can be rejected with 99% confidence.
	c.	The Null Hypothesis can be rejected with 90% confidence.
	d.	All of the above.

Answer 1

We can use T-test to test the following hypothesis

Null Hypothesis: There is no significant difference between sample mean and hypothesized mean

T-test statistic = (Sample Mean – Hypothesized Mean) ÷ ((Standard Deviation)/√N)

Sample mean = 254

Hypothesized mean = 252

Standard deviation = 20

N (sample size) = 1500

T-test statistic = (254 – 252) ÷ ((20/√1500)

T-test statistic = 2/0.516

T-test statistic = 3.87

The value of t statistic from t table for different levels of significance is following

Confidence Level	t value
90%	1.645
95%	1.960
99%	2.576

Since, the calculated t value of 3.87, is more than the table value of t for different significance level. So, the Null Hypothesis can be rejected with 90%, 95%, and 99% level of confidence. This means, there exists significant difference between the sample means and the hypothesized mean.