Question

A Hypothesis test 3) Jed raises chickens. He says that the average chicken weight is 5.5 lbs. Test his claim. A simple random sample, looks like it's from a Normal distribution of Jed's chickens was collected with the following data in pounds: 3.4, 5.8, 6.0, 4.2, 5.7.7.1,6.3,6.2, 5.1,7.2 (you find the stats)

Answer 1

From the given sample data :

The sample size is , n=10

The sample mean is , $\bar{X}=\frac{\sum X}{n}=5.7$

The sample standard deviation is , $s=\sqrt{\frac{\sum X^2-\frac{(\sum X)^2}{n}}{n-1}}=1.1935$

The null and alternative hypothesis is ,

$H_0:\mu=5.5;H_a:\mu\neq 5.5$

The test is two-tailed test.

Now , df=degrees of freedom=n-1=10-1=9

The critical values are , ; From t-table

tdf,a/2 t9,0.05/2 +2.262

The rejection rule is ,

Rejec Ho , if t-stat>2.262 or t-stat<-2.262 , otherwise fail to reject Ho.

The test statistic is ,

$t_{stat}=\frac{\bar{X}-\mu_0}{s/\sqrt{n}}=\frac{5.7-5.5}{1.1935/\sqrt{10}}=0.5299$

Decision : Here , t-stat=0.5299 < 2.262

Therefore , fail to reject Ho.

Conclusion : There is sufficient evidence to support the claim that the average chicken weight is 5.5 lbs.