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sadmomsclub
08.10.2020 •
Mathematics
A pharmaceutical company is interested in testing the effect of humidity on the weights of pills sold in a new aluminum package. Let X and Y denote the weight of a pill in the old aluminum package and in the new aluminum package (respectively) after the packaged pill has spent one week in chamber kept at 30 °C and 100 % humidity. Define a null and alternates hypothesis to test whether the old aluminum package pills weigh less than the new aluminum package pills following the humidity-chamber treatment. The following random samples of X yielded the following weights in milligrams:
373.2 376.7 381.6 382.1 388.7 384.0
397.9 389.8 385.1 371.3 383.5
and the following random sample of Y yielded the following weights in milligrams:
395.5 384.8 383.5 386.5 394.8
391.6 397.7 384.0 391.7 398.8
Define a critical region with a significance level of alpha = 0.05 and calculate the value of the test statistic. Accept or reject the null hypothesis and then state a scientific conclusion about the packaged-pill humidity experiment.
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Ответ:
The null hypothesis is![H_o : \mu_1 = \mu_2](/tpl/images/0794/2788/1d5dc.png)
The alternative hypothesis is![H_a : \mu_1 < \mu_2](/tpl/images/0794/2788/21964.png)
The test statistics is![t = -2.65](/tpl/images/0794/2788/7b749.png)
Reject the null hypothesis
There is sufficient evidence to conclude that the weight of the old aluminium package pills is less than the new aluminium pills.
Step-by-step explanation:
From the question we are told that
The data for X is 373.2 , 376.7 , 381.6 , 382.1 , 388.7 , 384.0 , 397.9 , 389.8 ,385.1 , 371.3 , 383.5
The data for Y is 395.5 , 384.8 , 383.5 , 386.5 ,394.8
, 391.6 , 397.7 , 384.0 , 391.7 , 398.8
Generally the sample mean for X is mathematically represented as
=>![\= x = \frac{373.2 +376.7 +\cdots + 383.5}{11}](/tpl/images/0794/2788/51ae0.png)
=>![\= x = 383.08](/tpl/images/0794/2788/82f77.png)
Generally the sample mean for Y is mathematically represented as
=>![\= y = \frac{395.5 +384.8 +\cdots + 398.8}{10}](/tpl/images/0794/2788/8b7ce.png)
=>![\= y = 390.89](/tpl/images/0794/2788/4560c.png)
Generally the standard deviation for X is mathematically represented as
=>![\sigma_1 = \sqrt{\frac{( 373.2 - 383.08)^2 +( 376.7 - 383.08)^2 +\cdots + ( 383.5 - 383.08)^2 }{11} }](/tpl/images/0794/2788/49ed5.png)
=>
Generally the standard deviation for Y is mathematically represented as
=>![\sigma_2 = \sqrt{\frac{( 395.5 - 390.89)^2 +( 384.8 - 390.89)^2 +\cdots + ( 398.8 - 390.89)^2 }{10} }](/tpl/images/0794/2788/20155.png)
=>
The null hypothesis is![H_o : \mu_1 = \mu_2](/tpl/images/0794/2788/1d5dc.png)
The alternative hypothesis is![H_a : \mu_1 < \mu_2](/tpl/images/0794/2788/21964.png)
Generally the test statistics is mathematically represented as
=>![t = \frac{383.08 - 390.89}{ \sqrt{\frac{7.63^2 }{ 11 } +\frac{5.82^2 }{10} } }](/tpl/images/0794/2788/5314c.png)
=>![t = -2.65](/tpl/images/0794/2788/7b749.png)
Generally the level of significance is![\alpha = 0.05](/tpl/images/0794/2788/224ae.png)
Generally the degree of freedom is mathematically represented as
=>![df = 11 + 10 - 2](/tpl/images/0794/2788/339a0.png)
=>![df = 19](/tpl/images/0794/2788/e9b8f.png)
Generally from the student t- distribution table the critical value of
at a df = 19 is
Now comparing the critical value obtained with test statistic calculated we see that the critical value is the region of the calculated test statistic( i.e between -2.65 and 2.65) hence we reject the null hypothesis
Therefore there sufficient evidence to conclude that the old aluminium package pills weight is less than the new aluminium pills
Ответ:
Add the cost of pansies to 15 and the cost of trees to 8. Then add them together.
Step-by-step explanation:
That's what I said and I got it correct so there you go, hope this helps.