) State the null hypothesis H, and the alternative hypothesis H,. Ho : 0 H :0

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(a) State the null hypothesis H and the alternative hypothesis H,.
H, :0
H :0
(b) Determine the type of test statistic to use.
t
Degrees of freedom: |
(c) Find the value of the test statistic. (Round to three or more decimal places.)
(d) Find the p-value. (Round to three or more decimal places.)
(e) Can we support the researchers' claim that the mean recovery time when
treated with multivitamin is not equal to the mean recovery time when
treated with placebo?
OYes ONo
Transcribed Image Text:(a) State the null hypothesis H and the alternative hypothesis H,. H, :0 H :0 (b) Determine the type of test statistic to use. t Degrees of freedom: | (c) Find the value of the test statistic. (Round to three or more decimal places.) (d) Find the p-value. (Round to three or more decimal places.) (e) Can we support the researchers' claim that the mean recovery time when treated with multivitamin is not equal to the mean recovery time when treated with placebo? OYes ONo
A random selection of volunteers at a research institute have been exposed to a typical cold virus. After they started to have cold symptoms, 15 of them were
given multivitamin tablets formulated to fight cold symptoms. The remaining 15 volunteers were given placebo tablets. For each individual, the length of time
taken to recover from the cold is recorded. At the end of the experiment the following data are obtained.
Days to recover from a cold
Treated with multivitamin 8.2, 6.6, 2.7, 7.2, 4.5, 2.8, 5.3, 4.2, 6.3, 5.0, 5.5, 5.5, 6.1, 5.5, 5.0
Treated with placebo
3.8, 5.7, 7.4, 6.2, 6.0, 3.9, 2.1, 3.5, 1.4, 4.9, 5.7, 6.7, 4.2, 4.0, 3.8
Send data to calculator
Send data to Excel
It is known that the population standard deviation of recovery time from a cold is 1.8 days when treated with multivitamin tablets, and the population standard
deviation of recovery time from a cold is 1.5 days when treated with placebo tablets. It is also known that both populations are approximately normally
distributed. The researchers claim that the mean recovery time, µ,, of the patients treated with multivitamin is not equal to the mean recovery time µ,, of the
patients who are treated with placebo tablets. At the 0.05 level of significance, is there enough evidence to support this claim? Perform a two-tailed test. Then
complete the parts below.
Carry your intermediate computations to at least three decimal places. (If necessary, consult a list of formulas.)
Transcribed Image Text:A random selection of volunteers at a research institute have been exposed to a typical cold virus. After they started to have cold symptoms, 15 of them were given multivitamin tablets formulated to fight cold symptoms. The remaining 15 volunteers were given placebo tablets. For each individual, the length of time taken to recover from the cold is recorded. At the end of the experiment the following data are obtained. Days to recover from a cold Treated with multivitamin 8.2, 6.6, 2.7, 7.2, 4.5, 2.8, 5.3, 4.2, 6.3, 5.0, 5.5, 5.5, 6.1, 5.5, 5.0 Treated with placebo 3.8, 5.7, 7.4, 6.2, 6.0, 3.9, 2.1, 3.5, 1.4, 4.9, 5.7, 6.7, 4.2, 4.0, 3.8 Send data to calculator Send data to Excel It is known that the population standard deviation of recovery time from a cold is 1.8 days when treated with multivitamin tablets, and the population standard deviation of recovery time from a cold is 1.5 days when treated with placebo tablets. It is also known that both populations are approximately normally distributed. The researchers claim that the mean recovery time, µ,, of the patients treated with multivitamin is not equal to the mean recovery time µ,, of the patients who are treated with placebo tablets. At the 0.05 level of significance, is there enough evidence to support this claim? Perform a two-tailed test. Then complete the parts below. Carry your intermediate computations to at least three decimal places. (If necessary, consult a list of formulas.)
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