Question

A consumer group claims that the average annual consumption of high fructose corn syrup by a person in the U.S. is 48.8 pounds. You believe it is higher. You take a simple random sample of 35 people in the U.S. and find an average of 53.8 pounds with a standard deviation of 4.4 pounds. Test at 1% significance. Round to the fourth

Answer 1

Answer:

$6.7159$

Step-by-step explanation:

$\mu=48.8\\n=35\\\bar{x}=53.8\\\sigma=4.4\\\alpha=1\%=0.01$

Null and alternative hypothesis :

$H_0:\mu=48.8\\H_a:\mu>48.8$

Test statistic,

$t=\frac{\bar{x}-\mu}{\frac{\sigma}{\sqrt{n}}}$

$\Rightarrow t=\frac{53.8-48.8}{\frac{4.4}{\sqrt{35}}}$

$\Rightarrow t=\frac{5\times 5.91}{4.4}$

$\Rightarrow t=6.715$

Test statistic $t=6.715$

$P-$value $=P(t>6.715)$

$P-$ value $=0.0001$  by the p- table

Significance level $0.01$

         $p-$value

  We reject $H_0$