# Test the claim that each bag of the farmers potatoes are 60 pounds?

Problem: A farmer sells sacks of potatoes at a county fair. Each bag is labeled 60 pounds. The fair organizers employ a statistician to verify that all business is conducted accurately. The statistician selects 50 sacks of the farmer's potatoes and finds a sample mean of 57 pounds. The standard deviation is 8 pounds. Test the claim that the sacks do not contain 60 pounds at the .05 significance level.

Identify the following:

A) Ho (Null hypothesis).

1. Critical Value

B) Test Statistic (show calculation)

C) Your conclusion about the null hypothesis

D) Your statement about the claim

https://brainmass.com/statistics/hypothesis-testing/test-claim-each-bag-farmers-potatoes-13209

## SOLUTION This solution is **FREE** courtesy of BrainMass!

Problem: A farmer sells sacks of potatoes at a county fair. Each bag is labeled 60 pounds. The fair organizers employ a statistician to verify that all business is conducted accurately. The statistician selects 50 sacks of the farmer's potatoes and finds a sample mean of 57 pounds. The standard deviation is 8 pounds. Test the claim that the sacks do not contain 60 pounds at the .05 significance level.

Identify the following:

A) Ho (Null hypothesis).

1. Critical Value

Null hypothesis : Mean=M = 60 pounds

Critical value z=

Z at the 0.05 level of significance 1 tailed test = -1.6448

B) Test Statistic (show calculation)

sample mean= 57

Hypothesized Mean=M = 60 pounds

Standard deviation =s= 8 pounds

sample size=n= 50

sx=standard error of mean=s/square root of n= 1.1314

Significance level=alpha (a) = 0.05

No of tails= 1

Since sample size= 50 > = 30 use normal distribution

Test statistic

z=(sample mean-M )/sx= -2.6516

C) Your conclusion about the null hypothesis

Reject Null Hypothesis since test statistic is outside the accepatnce region ( beyond critical value)

D) Your statement about the claim

Accept the alternative hypothesis that the sacks do not contain 60 pounds at the .05 significance level

Accept the claim

https://brainmass.com/statistics/hypothesis-testing/test-claim-each-bag-farmers-potatoes-13209