Mathematics, 24.03.2021 17:20 jonathan3191

The Westbrook Pharmaceutical Company manufactures atorvastatin pills, designed to lower cholesterol levels. Listed below are the amounts (in mg) of atorvastatin in a random sample of the pills. Use a 0.05 significance level to test the claim that the pills come from a population in which the amount of atorvastatin is equal to 25mg. 24.1, 24.4, 24.3, 24.9, 24.1, 26.2, 25.1, 24.7, 24.4, 25.0, 24.7, 25.1, 25.3, 25.5, 25.5

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Answer from: april861

Solution :

Given :

$\mu = 24$

n = 15

$\overline x = 24.89$

s = 0.5902

The hypothesis :

$H_0 : \mu = 25$

$H_a : \mu \neq 25$

This is a 2 tailed test.

The significance level is $95 \% \ ( \alpha =0.05)$

The test statistic :

$Z=\frac{\overline x - \mu}{\frac{\sigma}{\sqrt n}}$

$Z=\frac{24.89-25}{\frac{0.5902}{\sqrt 15}}$

= -0.72

The p value : The p value for Z = -0.72 is 0.4716

The critical value : the critical value at α = 0.05 is +1.96 to -1.96

The decision rule :

If $Z_{observed} Z_{critical}$ or if $Z_{observed} < -Z_{critical}$ , then reject $H_0$ .

Also if p value is less than α, then reject $H_0$ .

The decision :

Since the Z falls in between +1.96 and -1.96, we fail to reject the $H_0$ . Also since p value is greater than α, we fail to reject $H_0$ .

The conclusion :

There is not sufficient evidence at the 95% significance level to warrant rejection of the claim that the pills come from a population in which the amount of the atorvastatin is equal to 25 mg.

Now calculating the mean and the standard deviation :

$\text{Mean} = \frac{\text{sum of observation}}{\text{total observations}}$

Standard deviation = $\sqrt{\text{variance}}$

Variance = $\frac{\text{sum of squares(SS)}}{n-1}$

Where, SS = $\sum (X - \text{mean})^2$

X Mean $(X-\text{mean})^2$

24.1 24.89 0.62

24.4 24.89 0.24

24.3 24.89 0.35

24.9 24.89 0

24.1 24.89 0.62

24.2 24.89 1.72

24.1 24.89 0.04

26.2 24.89 0.04

25.1 24.89 0.24

25 24.89 0.01

24.7 24.89 0.04

25.1 24.89 0.04

25.3 24.89 0.17

25.5 24.89 0.37

n 15

Sum 373.3

Average 24.89

SS 4.8775

Variance = $\frac{SS}{n-1}$ 0.348392857

Standard deviation 0.5902

Answer from: Quest

the answer on e2020 is

4/5

3/5

4/3

step-by-step explanation:

Answer from: Quest

the least common denominatore of 7 and 2 is 9

step-by-step explanation:

7+2=9

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