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A new sleeping pill is advertised to increase the daily sleeping time of insomniacs by an average of 3.0 hours, with a variance of 0.27. A government group conducts an independent study on the new pill, claiming that the actual variance, oʻ, of increase in sleeping time is higher than the advertised variance. The government group tests 20 insomniacs, chosen at random, with the new pill. The insomniacs report a mean daily sleeping increase of 2.9 hours, with a variance of 0.35. Is there enough evidence to conclude, at the 0.1 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 Ho and the alternative hypothesis H· Ho :0 H, :0 |(b) Determine the type of test statistic to use. (Choose one) ▼ O=0 OSO |(c) Find the value of the test statistic. (Round to three or more decimal places.) O

A new sleeping pill is advertised to increase the daily sleeping time of insomniacs by an average of 3.0 hours, with a variance of 0.27. A government group conducts an independent study on the new pill, claiming that the actual variance, oʻ, of increase in sleeping time is higher than the advertised variance. The government group tests 20 insomniacs, chosen at random, with the new pill. The insomniacs report a mean daily sleeping increase of 2.9 hours, with a variance of 0.35. Is there enough evidence to conclude, at the 0.1 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 Ho and the alternative hypothesis H· Ho :0 H, :0 |(b) Determine the type of test statistic to use. (Choose one) ▼ O=0 OSO |(c) Find the value of the test statistic. (Round to three or more decimal places.) O

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter4: Equations Of Linear Functions
Section: Chapter Questions
Problem 8SGR
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A new sleeping pill is advertised to increase the daily sleeping time of insomniacs by an average of 3.0 hours, with a variance of 0.27. A government group conducts an independent study on the new pill, claiming that the actual variance, o, of increase in sleeping time is higher than the advertised variance. The government group tests 20 insomniacs, chosen at random, with the new pill. The insomniacs report a mean daily sleeping increase of 2.9 hours, with a variance of 0.35. Is there enough evidence to conclude, at the 0.1 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,. p Họ :0 H :0 (b) Determine the type of test statistic to use. (Choose one) v O=0 OSO (c) Find the value of the test statistic. (Round to three or more decimal places.) O<O (d) Find the p-value. (Round to three or more decimal places.) (e) Can we support the claim that the variance of increase in sleeping time using the new pill is higher than the one advertised? O Yes ONo
Transcribed Image Text:A new sleeping pill is advertised to increase the daily sleeping time of insomniacs by an average of 3.0 hours, with a variance of 0.27. A government group conducts an independent study on the new pill, claiming that the actual variance, o, of increase in sleeping time is higher than the advertised variance. The government group tests 20 insomniacs, chosen at random, with the new pill. The insomniacs report a mean daily sleeping increase of 2.9 hours, with a variance of 0.35. Is there enough evidence to conclude, at the 0.1 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,. p Họ :0 H :0 (b) Determine the type of test statistic to use. (Choose one) v O=0 OSO (c) Find the value of the test statistic. (Round to three or more decimal places.) O<O (d) Find the p-value. (Round to three or more decimal places.) (e) Can we support the claim that the variance of increase in sleeping time using the new pill is higher than the one advertised? O Yes ONo
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