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

`6.7159`

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}{(\sigma)/(√(n))}`

`\Rightarrow t=(53.8-48.8)/((4.4)/(√(35)))`

`\Rightarrow t=(5* 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
`<0.01`

We reject
`H_0`