A new sleeping pill is advertised to increase the daily sleeping time of insomniacs by an average of

2.9

hours, with a standard deviation of

0.52

. A government group conducts an independent study on the new pill, claiming that the actual standard deviation,

, of increase in sleeping time is different from the advertised standard deviation. The government group tests

19

insomniacs, chosen at random, with new pill. The insomniacs report a mean daily sleeping increase of

2.8

hours, with a standard deviation of

0.37

. Is there enough evidence to conclude, at the

0.05

level of significance, that the government group is correct? Assume that the increase in the sleeping time provided by the new pill is normally distributed.

Perform a two-tailed test.

(a)	State the null hypothesis H0 and the alternative hypothesis H1 .
H0:
H1:
(b)	Determine the type of test statistic to use.
	(Choose one)
(c)	Find the value of the test statistic. (Round to three or more decimal places.)
(d)	Find the two critical values. (Round to three or more decimal places.)
and
(e)	Can we support the claim that the standard deviation of increase in sleeping time using the new pill is different from the one advertised?
Yes No