Assessment Progress 70 57 66 56 58 56 52 50 73 82 45 33 24 4

Assessment Progress

7.0, 5.7, 6.6, 5.6, 5.8, 5.6, 5.2, 5.0, 7.3, 8.2

4.5, 3.3, 2.4, 4.4, 3.9, 3.7, 6.5, 6.8, 3.7, 3.4

Carry your intermediate computations to at least three decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.)

The null hypothesis: H0:

The alternative hypothesis: H1:

The type of test statistic:

(Choose one)

Z, t, Chi square, F

The value of the test statistic:
(Round to at least three decimal places.)

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?

Yes or No

Question #3 Assessment Progress A random selection of volunteers at a research institute have been exposed to a typical cold virus. After they started to have cold symptoms, of them were given multivitamin tablets daily which contain grams of vitamin C and various other vitamins and minerals. The remaining volunteers were given placebo tablets. For each individual, the length of time taken to recover from cold is recorded. At the end of the experiment following data are obtained: Days to recover from cold Treated with multivitamin 7.0, 5.7, 6.6, 5.6, 5.8, 5.6, 5.2, 5.0, 7.3, 8.2 Treated with placebo 4.5, 3.3, 2.4, 4.4, 3.9, 3.7, 6.5, 6.8, 3.7, 3.4 Send data to Excel It is known that the population standard deviation of recovery time from cold is days when treated with multivitamin, and the population standard deviation of recovery time from cold is 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, , of the patients treated with multivitamin is not equal to the mean recovery time , of the patients who are treated with placebo tablets. At the level of significance, is there enough evidence to support this claim? Perform a two-tailed test. Then fill in the table below. Carry your intermediate computations to at least three decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.)

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u1 - u2   =   0  
Ha:   u1 - u2   =/   0  
At level of significance =    0.05          
As we can see, this is a    two   tailed test.  
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WE USE A T STATISTIC HERE. [ANSWER, TYPE OF TEST STATISTIC]

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Now, the critical value for t is, as df = n1 + n2 - 2 = 18, by table/technology              
              
tcrit =    +/- 2.10092204   [ANSWER]  

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Calculating the means of each group,              
              
X1 =    6.2          
X2 =    4.26          
              
Calculating the standard deviations of each group,              
              
s1 =    1.8          
s2 =    1.5          
              
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):              
              
n1 = sample size of group 1 =    10          
n2 = sample size of group 2 =    10          
Thus, df = n1 + n2 - 2 =    18          
Also, sD =    0.740945342          
              
Thus, the t statistic will be              
              
t = [X1 - X2 - uD]/sD =    2.618276801   [TEST STATISTIC]      
              
where uD = hypothesized difference =    0          
              
Thus, as our t is not between the two critical values, we decide to   WE REJECT THE NULL HYPOTHESIS.          
              
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YES, 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. [ANSWER]