Question

In a controlled and scientifically valid study of sleeping pills, 40 people who took Pill A averaged 7.5 hours of sleep with a standard deviation of 1.5 hours, while 40 people who took Pill B is averaged 8 hours of sleep, with a standard deviation of 2 hours. Is there enough evidence to support the assertion that Pill B is more effective than Pill A to a 95% confidence interval? Explain.

Answer 1

Df = (s1^2/n1 + s2^2/n2)^2/((s1^2/n1)^2/(n1 - 1) + (s2^2/n2)^2/(n2 - 1))

= ((1.5)^2/40 + (2)^2/40)^2/(((1.5)^2/40)^2/39 + ((2)^2/40)^2/39) = 72

At 95% confidence interval the critical value is t^* = 1.993

The 95% confidence interval is

+/- t^* * sqrt(s1^2/n1 + s2^2/n2)

= (7.5 - 8) +/- 1.993 * sqrt((1.5)^2/40 + (2)^2/40)

= -0.5 +/- 0.7878

= -1.2878, 0.2878

Since the interval contains 0, so there is not enough evidence to support the assertion that pill B is more effective than pill A.