Answer to Question #140533 in Microeconomics for Joe Seri

Question

The amount of Mangoes that are produced each year by a farmer in Waka Village is normally
distributed. The standard deviation of the bags of mangoes is identified as 0.04 grams.
Mangoes that too small and unripe are not bagged. Using your knowledge of hypothesis testing
and a 95% confidence level, execute a two – tailed to prove the claim that μ = 0.50 grams. The
sample mean is 0.51 grams and the sample size is 25 bags of mangoes.

Answer 1

Null hypothesis (H₀): Mangoes that are too small and unripe are not bagged.

Alternative hypothesis (H_A): Mangoes that not too small and unripe are bagged.

s.d = 0.04

α=0.05

μ = 0.50 grams

x = 0.51 grams

n = 25

t = $\frac{x - µ}{s.e}$

s.e = $\frac{s.d}{√n}$

s.e = $\frac{0.04}{√25}$

s.e = 0.008

t = $\frac {0.51 – 0.50}{0.008}$

Tstatistic = 1.25

From statistical tables,

d.f = n-1 = 25-1 = 24

Tcritical = 2.064

Inference

Since Tcritical is greater than the Tstatistic (2.064 >1.25), the null hypothesis should not be rejected. There is 95 percent confidence that the mangoes that are too small and unripe are not bagged.