(7(21) Workers at a certain soda drink factory collected data on the volumes (in
ID: 3310491 • Letter: #
Question
(7(21) Workers at a certain soda drink factory collected data on the volumes (in ounces) of a simple random sample of 19 cans of the soda drink. Those volumes have mean of 12.19 oz and a standard deviation of 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 0.05 significance level. What is the sampling distribution of the sample statistic you want to use and why? e) 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. f) Perform the hypothesis test using the p-value method. g) What is your conclusion using ()? Explain your conclusion in words.Explanation / Answer
mean = 12.19
std. dev. = 0.11
n = 19
a)
Range = 12.70 - 12.02 = 0.68
As per range rule, sigma = range/4 = 0.68/4 = 0.17
b)
The distribution of will be used is chi-square because chi-square distribution is used for the purpose of hypothesis test of single sample sigma
c)
H0: sigma = 0.17
H1: sigam < 0.17
d)
Rejection region is below 9.390 for chi-square test statistics
e)
Test statistics, chi-square = (N-1)(s/sigma)^2 = (19-1)*(0.11/0.17)^2 = 7.5363
f)
p-value = 0.0152
g)
As p-value is less than significance level of 0.05, we reject the null hypothesis. This means there are significant evidence to conclude that std.dev. is less than 0.17
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