Question

Homework: 7.2 Score: 0 of 1 pt 7.2.35 14 of 14 (0 complete) HW Score: 0%, 0 of 14 pts Question Help caffeine content per 12-ounce bottle of cola is 35 milligrams You want to test this claim Duning your tests, you of thirty 12-ounce botties of cola has a mean caffeine content of 32.9 milligrams with a standard deviation of 6 9 milligrams Al a002, can A company that makes cola drinks states that the mean you reject the company's claim? Complete parts (a) through (e) ??, ?? p232 9 Ha ?-329 Ha u 32 5 Ha ?.35 Ha ?#329 Ha ?-35 Ha la#35 5

Answer 1

Given datas

the claim of the company that the caffeine present per 12 ounce bottel (population mean) $\mu =35$

no of sample taken (n)=30

caffeine present per 12 ounce bottel found in sample (Sample mean) $\bar{X}=32.9$

Sample standard daviation S=6.9

$\alpha =0.02$

So the claim is $\mu =35$

a)so the hypothesis will be

(f)

$H_{o}\rightarrow \mu =35$

$H_{a}\rightarrow \mu \neq 35$

now we have to check the claim so for that

Z score =    $Z=\frac{\bar{X}-\mu }{S}=\frac{32.9-35}{6.9}=0.30$

now we have $\alpha =0.02$

for $\alpha =0.02$ the Z criticle value

$Z_{c}=\pm 2.33$

since it is two tailed test so we have to check that valu Z score is within this criticle region or not

since -2.33<0.30<+2.33

so our test static lie within the criticle region in the bell shape curve so we can say that we dont have sufficient prove to reject our alternative hypothesis .

conclusion :--As we are not able reject our assumption i.e. $\mu \neq 35$

so we can say that we have enough evidence to reject the companies claim (i.e. null hypothesis ) that $\mu =35$