Question

What price do farmers get for their watermelon crops? In the third week of July, a random sample of 40 farming regions gave a sample mean cost of 6.90 (in dollars per 100 pounds of watermelon). Suppose that the population standard deviation of the cost in July is 1.65 (in dollars per 100 pounds of watermelon). Is the sample data sufficient to show that the population mean cost of watermelon crops in July is more than 6.00 dollars per 100 pounds of watermelon? Use α = 0.05. -

Find the H0 and H1 Find the P-Value

Answer 1

Solution :

= 6.00

= 6.90

=1.65

n = 40

This is the right tailed test .

The null and alternative hypothesis is ,

H₀ :    = 6.00

H_a : > 6.00

Test statistic = z

= ( - ) / / n

= ( 6.90-6.00) / 1.65 / 40

= 3.45

Test statistic = z = 3.45

P(z >3.45 ) = 1 - P(z < 3.45 ) = 1 -0.9997

P-value =0.0003

= 0.05  

P-value <

0.0003 < 0.05

Reject the null hypothesis .

There is sufficient evidence to suggest that