Watch Dog - statistics Report
Describe the scenario outlined in the consumer watchdog problem and the actions taken by you (statistics person) to advise your boss (store owner) to make a deal with the crafty salesman.
Cans of salmon are supposed to have a net weight of 6 oz. The canner says that the net weight is a random variable with mean µ = 6.02 oz and std. dev. σ = .18 oz. Suppose you take a random sample of 36 cans and calculate the sample weight to be 5.97 oz. Find the probability that the mean weight of the sample is less than or equal to 5.97 oz.
Watch dog
Example 5
Cans of salmon are supposed to have a net weight of 6 oz. The canner says that the net weight is a random variable with mean =6.05 oz. and stand. dev. o=.18 oz.
Suppose you take a random sample of 36 cans and calculate the sample mean weight to be 5.97 OZ.
Find the probability that the mean weight of the sample is less than or equal to 5.97 oz.
Population X: amount of salmon in a can E(x)=6.05 oz, SD(x) = .18 oz
• X sampling dist: E(x)=6.05 SD(x)=.18/6=.03 - By the CLT, X sampling dist is approx. normal
• P(X ≤ 5.97) = P(z ≤ [5.97-6.05]/.03) =P(z ≤-.08/.03)=P(z ≤ -2.67)=.0038
How could you use this answer?
Suppose you work for a “consumer watchdog” group
If you sampled the weights of 36 cans and obtained a sample mean x ≤ 5.97 oz., what would you think?
Since P(× ≤ 5.97) = .0038, either:
- you observed a “rare” event (recall: 5.97 oz is 2.67 stand. dev. below the mean) and the mean fill E(x) is in fact 6.05 oz. (the value claimed by the canner)
- the true mean fill is less than 6.05 oz., (the canner is lying ).
Use at least 750 words and have a Turn-it-in similarity report with no more than 20%. Use the following outline:
- Introduction
- Decision made by using probability inference base on likelihood.
- Decision made by using probability inference base on 98% confidence interval.
- Decision made by using probability inference base on Hypothesis testing with α = .05 (using p-value method).
- Decision made by using probability inference base on Hypothesis testing with α = .05 (using the classic method).
- Conclusion
- References.