A new sleeping pill is advertised to increase the daily sleeping time of insomniacs by an average of 2.8 hours, with a standard deviation of 0.60. A government group conducts an independent study on the new pill, claiming that the actual standard deviation, o, of increase in sleeping time is higher than the advertised standard deviation. The government group tests 23 insomniacs, chosen at random, with the new pill. The insomniacs report a mean daily sleeping increase of 2.7 hours, with a standard deviation of 0.83. Is there enough evidence to conclude, at the 0.01 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 one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified below. (If necessary, consult a list of formulas.) (a) State the null hypothesis H, and the alternative hypothesis H . H p Ho : 0 X S p H, : I O (b) Determine the type of test statistic to use. Degrees of freedom: 0=0 030 020 (c) Find the value of the test statistic. (Round to three or more decimal places.) 0* 00 X 5 ? (d) Find the p-value. (Round to three or more decimal places.) 0 (e) Can we support the claim that the standard deviation of increase in sleeping time using the new pill is higher than the one advertised? Yes ONo