Question

Researchers studying the effect of diet on growth would like to know if a vegetarian diet affects the height of a child. Twelve students are randomly selected that are all 6-years old. The average height of these kids is 42.5 inches with a standard deviation of 3.8 inches. The average height of all 6-year old kids is found to be 45.75 inches. Conduct a hypothesis test to determine if there is overwhelming evidence at alpha = .05 that 6-year old vegetarian kids are not the same height as other six year-old kids. Determine the critical values, test statistic and any specific information from the problem.

Answer 1

Answer:

a)  $t_{0.035},11=\pm2.201$

b)  $t=-2.963$

c)  $Reject\ H_0\ when\ \alpha=0.05$

d)   $t$

   $-2.963$

Step-by-step explanation:

From the question we are told that:

Sample size $n=12$

Mean $\=x=42.5$

Standard deviation $\sigma=3.8$

Population mean $\mu=45.75$

Significance $\alpha=0.05$

 

Generally the hypothesis given by

$H_0;\mu=45.75\\H_1:\neq =45.75$

Generally the equation for test statistics is mathematically given by

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

$t=\frac{42.5-45.75}{3.8/\sqrt{12} }$

$t=-2.963$

Generally the Critical value is mathematically given by

$t_{\alpha/2},d_t$

$\alpha=0.05 \\\alpha/2=0.025\\d_t=n-1=11$

$t_{0.035},11$

From table

$t_{0.035},11=\pm2.201$

Therefore

$t$

$-2.963$

$Reject\ H_0\ when\ \alpha=0.05$