Question

The meat department of a local supermarket chain packages ground beef in trays of two sizes. The smaller tray is intended to hold 1 kilogram (kg) of meat. A random sample of 40 packages in the smaller meat tray produced weight measurements with an average of 1.01 kg and a standard deviation of 19 grams.

(a) If you were the quality control manager and wanted to make sure that the average amount of ground beef was indeed 1 kg, what hypotheses would you test?

H₀: μ < 1 versus H_a: μ > 1H₀: μ = 1 versus H_a: μ < 1    H₀: μ ≠ 1 versus H_a: μ = 1H₀: μ = 1 versus H_a: μ > 1H₀: μ = 1 versus H_a: μ ≠ 1

(b) Find the p-value for the test and use it to perform the test in part (a). (Round your answer to four decimal places.)
p-value =  

State your conclusion. (Use α = 0.05.)

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

(c) How would you, as the quality control manager, report the results of your study to a consumer interest group?

There is insufficient evidence to indicate that the average amount of ground beef is different from 1 kilogram.There is sufficient evidence to indicate that the average amount of ground beef is different from 1 kilogram.    There is a 95% chance that any meat tray selected will weigh 1 kilogram.Since the sample average is greater than 1, all meat trays will weigh at least 1 kilogram.There is a 5% chance that any meat tray selected will weigh 1 kilogram.

Answer 1

a)  what hypotheses would you test?

H0: μ = 1 versus Ha: μ ≠ 1

b) Find the p-value for the test and use it to perform the test in part (a)

Test Statistic :-

P value

Looking the value t = 3.3287 in t table across n-1 = 40-1 degree of freedom

t = 3.3287 lies between the value 3.307 and 3.551 with respective p value are 0.002 and 0.001

using excel to calculate exact P value = 0.0019

State your conclusion. (Use α = 0.05.)

Reject null hypothesis if P value < α = 0.05 level of significance

0.0019 < 0.05, we reject null hypothesis

Conclusion :- Accept Alternative Hypothesis  

c)  results of your study  μ ≠ 1

There is sufficient evidence to indicate that the average amount of ground beef is different from 1 kilogram.