A manufacturer of chocolate candies uses machines to package candies as they move along a filling line.Although the packages are labeled as 8 ounces,the company wants the packages to contain a mean of 8.17 ounces so that virtually none of the packages contain less than 8 ounces.A sample of 50 packages is selected periodically,and the packaging process is stopped if there is deviation of 0.059 ounce.Complete parts (a)and(b) Determine the test statistic. The test statistic is
Question
A manufacturer of chocolate candies uses machines to package candies as they move along a filling line.Although the packages are labeled as 8 ounces,the company wants the packages to contain a mean of 8.17 ounces so that virtually none of the packages contain less than 8 ounces.A sample of 50 packages is selected periodically,and the packaging process is stopped if there is deviation of 0.059 ounce.Complete parts (a)and(b) Determine the test statistic. The test statistic is
Solution
To determine the test statistic, we need to use the formula for the z-score:
Z = (X - μ) / (σ/√n)
Where: X = sample mean μ = population mean σ = standard deviation n = sample size
From the problem, we know: μ = 8.17 ounces (the company wants the packages to contain a mean of 8.17 ounces) σ = 0.059 ounces (the deviation) n = 50 packages (a sample of 50 packages is selected periodically)
However, we don't have the sample mean (X) given in the problem. We need this information to calculate the test statistic.
If the sample mean was provided, you would substitute these values into the formula to calculate the z-score, which is the test statistic.
Similar Questions
A manufacturer of chocolate candies uses machines to package candies as they move along a filling line.Although the packages are labeled as 8 ounces,the company wants the packages to contain a mean of 8.17 ounces so that virtually none of the packages contain less than 8 ounces.A sample of 50 packages is selected periodically,and the packaging process is stopped if there is deviation of 0.059 ounce.Complete parts (a)and(b) State the null and alternative hypotheses. H0μ= 8.17 H1:μ≠8.17 Determine the test statistic. The test statistic is
A manufacturer of chocolate candies uses machines to package candies as they move along a filling line.Although the packages are labeled as 8 ounces,the company wants the packages to contain a mean of 8.17 ounces so that virtually none of the packages contain less than 8 ounces.A sample of 50 packages is selected periodically,and the packaging process is stopped if there is evidence that the mean amount packaged is different from 8.17 ounces.Suppose that in a particular sample of 50 packages,the mean amount dispensed is 8.171 ounces,with a sample standard deviation of 0.053 ounce.Complete parts (a)and (b). Click here to view page 1 of the critical values for the t Distribution. Click here to view page 2 of the critical values for the t Distribution. a.Is there evidence that the population mean amount is different from 8.17 ounces?(Use a 0.10 level of significance.) State the null and alternative hypotheses H0:μ=8.17 H1:μ≠8.17 (Type integers or decimals. Identify the critical value(s). The critical value(s)is(are) (Round to four decimal places as needed.Use a comma to separate answers as needed.)
contain a mean of 8.17 ounces so that virtually none of the packages contain less than 8 ounces.A sample of 50 packages is selected periodically,and the packaging process is stopped if there is evidence that the mean amount packaged is different from 8.17 ounces.Suppose that in a particular sample of 50 packages,the mean amount dispensed is 8.171 ounces,with a sample standard deviation of 0.053 ounce.Complete parts (a)and(b) Click here to view page 1 of the critical values for the t Distribution. Click here to view page 2 of the critical values for the t Distribution. 回 a.Is there evidence that the population mean amount is different from 8.17 ounces?(Use a 0.10 level of significance. State the null and alternative hypotheses.
The makers of Mini-Oats cereal have an automated packaging machine that is set to fill boxes with 24 ounces of cereal.At various times in the packaging process, we select a random sample of 100 boxes to see whether or not the machine is filling the boxes with an average of 24 ounces of cereal.Which of the following is a statement of the alternative hypothesis? The machine fills the boxes with the proper amount of cereal. The average is less than 24 ounces. The machine fills the boxes with the proper amount of cereal. The average is 24 ounces. The machine is not filling the boxes with the proper amount of cereal. The average is not 24 ounces.Question 4
The makers of Mini-Oats cereal have an automated packaging machine that is set to fill boxes with 24 ounces of cereal. At various times in the packaging process, we select a random sample of 100 boxes to see whether or not the machine is filling the boxes with an average of 24 ounces of cereal.Which of the following is a statement of the null hypothesis? The machine is not filling the boxes with the proper amount of cereal. The average is not 24 ounces. The machine is not putting enough cereal in the boxes. The average is less than 24 ounces. The machine fills the boxes with the proper amount of cereal. The average is 24 ounces.
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