Answer to Question #115692 in Statistics and Probability for juan

Question

The weights (lb) of discarded plastic from a sample of households are 62 with a mean of 1,911 lb and the standard deviation is 1,065 lb. Use a 0,05 significance level to test the claim that the mean weight of discarded plastic from the population is greater than 1,800 lb.

Answer 1

Null hypothesis $H_0:\mu=1800.$

Alternative hypothesis $H_a:\mu>1800.$

Test statistic: $z=\frac{\bar x-\mu}{\frac{\sigma}{\sqrt{n}}}=\frac{1911-1800}{\frac{1065}{\sqrt{62}}}=0.82.$

P-value: $p=P(Z>0.82)=0.206.$

Since the P-value is greater than 0.05, fail to reject the null hypothesis.