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

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

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