rkers at a certain soda drink factory collected data on the volumes (in ounces)
ID: 3311128 • Letter: R
Question
rkers at a certain soda drink factory collected data on the volumes (in ounces) of a simple random deviation of sample of 25 cans of the soda drink. Those volumes have a mean of 12.19 oz and a standard 0.11 oz, and they appear to be from a normally distributed population a The workers want the filling process to work so that almost all cans have volumes between 12.02 oz and 12.70 oz. If you use the range rule of thumb to estimate that the population standard deviation (o), less than or equal to what value should be? b) You wish to test the claim that the population of volumes has a standard deviation less than what you find in (a) using a 0.025 significance level. What is the sampling distribution of the sample statistic you want to use and why? c) Set up the null and alternative hypotheses clearly Ho: d) Determine the rejection and non-rejection regions based on your hypotheses in (c). State the critical value. e) Calculate the value of the test statistic. 1 Perform the hypothesis test using the p-value method. g) What is your conclusion using ()? Explain your conclusion in words.Explanation / Answer
a)
Range = 12.70 - 12.02 = 0.68
std. dev. = range/4 = 0.68/4 = 0.17
b)
Chi square distribution is used for the single sample/population standard deviation test
c)
H0: sigma = 0.17
H1: sigma < 0.17
d)
Rejection region is below the test statistics 12.4011
Hence critical value is 12.4011
e)
Test statistics, chi-square = (25-1)*(0.11/0.17)^2 = 10.0484
f)
p-value = 0.00566
g)
As p-value is less than he significance level of 0.025, we reject the null hypothesis
This means there are significant evidence to conclude that the standard deviation is less than 0.17
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