The manufacturer of Ice Melt claims that its products will melt snow and ice at temperatures as low as 0 ° Fahrenheit. A representative for a large chain of hardware stores is interested in testing this claim. The chain purchases a large shipment of 5-pound bags for distribution. The representative wants to know, with 95 % confidence and within ± 0.05 , what proportion of bags of Ice Melt perform the job as claimed by the manufacturer. a. How many bags does the representative need to test? What assumption should be made concerning the population proportion? (This is called destructive testing: i. e., the product being tested is destroyed by the test and is then unavailable to be sold.) b. Suppose that the representative tests 50 bags, 42 of then do the job as claimed. Construct a 95% confidence interval estimate for the population proportion that will do the job as claimed. c. How can the representative use the results of (b) to determine whether to sell the Ice Melt Product?
The manufacturer of Ice Melt claims that its products will melt snow and ice at temperatures as low as 0 ° Fahrenheit. A representative for a large chain of hardware stores is interested in testing this claim. The chain purchases a large shipment of 5-pound bags for distribution. The representative wants to know, with 95 % confidence and within ± 0.05 , what proportion of bags of Ice Melt perform the job as claimed by the manufacturer. a. How many bags does the representative need to test? What assumption should be made concerning the population proportion? (This is called destructive testing: i. e., the product being tested is destroyed by the test and is then unavailable to be sold.) b. Suppose that the representative tests 50 bags, 42 of then do the job as claimed. Construct a 95% confidence interval estimate for the population proportion that will do the job as claimed. c. How can the representative use the results of (b) to determine whether to sell the Ice Melt Product?
Solution Summary: The author determines the sample size required to estimate the population proportion of ice bags that perform the job.
The manufacturer of Ice Melt claims that its products will melt snow and ice at temperatures as low as
0
°
Fahrenheit. A representative for a large chain of hardware stores is interested in testing this claim. The chain purchases a large shipment of 5-pound bags for distribution. The representative wants to know, with
95
%
confidence and within
±
0.05
,
what proportion of bags of Ice Melt perform the job as claimed by the manufacturer.
a. How many bags does the representative need to test? What assumption should be made concerning the population proportion? (This is called destructive testing: i. e., the product being tested is destroyed by the test and is then unavailable to be sold.)
b. Suppose that the representative tests 50 bags, 42 of then do the job as claimed. Construct a 95% confidence interval estimate for the population proportion that will do the job as claimed.
c. How can the representative use the results of (b) to determine whether to sell the Ice Melt Product?
Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.