6) Company officials were concerned about the length of time a particular drug product retained its potency. A random sample of $n_1 = 10$ bottles of the product was drawn from the production line and analyzed for potency. A second sample of $n_2 = 10$ bottles was obtained and stored in a regulated environment for a period of 1 year. The readings obtained from each sample are given in the following table. \begin{tabular}{c|cccccccccc} & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\ \hline Fresh & 10.2 & 10.5 & 10.3 & 10.8 & 9.8 & 10.6 & 10.7 & 10.2 & 10.0 & 10.6 \\ Stored & 9.8 & 9.6 & 10.1 & 10.2 & 10.1 & 9.7 & 9.5 & 9.6 & 9.8 & 9.9 \\ \end{tabular} It is assumed that the potencies for the fresh and stored bottles follow normal distributions with the same population variance. (a) State appropriate hypotheses to test whether there is a difference in mean potency between the fresh and stored bottles; (b) Define the rejection region that has a significance level of $\alpha = 0.05$; (c) Perform an appropriate test for the hypotheses; (d) State your conclusion at $\alpha = 0.05$.
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- Null Hypothesis (\(H_0\)): There is no difference in mean potency between the fresh and stored bottles. Mathematically, \(H_0: \mu_1 = \mu_2\). - Alternative Hypothesis (\(H_a\)): There is a difference in mean potency between the fresh and stored bottles. Show more…
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Company officials were concerned about the length of time a particular drug product retained its potency. A random sample of n1 = 10 bottles of the product was drawn from the production line and analyzed for potency. A second sample of n2 = 10 bottles was obtained and stored in a regulatory environment for a period of 1 year. The readings (and summary statistics) obtained from each sample are given in the tables below: Potency Readings Fresh 10.2, 10.5, 10.3, 10.8, 9.8, 10.6, 10.7, 10.2, 10.0, 10.6 Stored 9.8, 9.6, 10.1, 10.2, 10.1, 9.7, 9.5, 9.6, 9.8, 9.9 - Find the mean and standard deviation for each group. - Estimate μ1 - μ2 using a 95% confidence interval. Comment on your findings. - Is there a statistically significant difference in mean potencies for the two bottle groups? Explain.
James K.
11) A bottling company produces bottles that hold 12 ounces of liquid. Periodically, the company gets complaints that their bottles are not holding enough liquid. To test this claim, the bottling company randomly samples 25 bottles and finds the average amount of liquid held by the bottles is 11.8 ounces with a standard deviation of .4 ounce. Which of the following is the set of hypotheses the company wishes to test? A) H0: μ = 12 vs. Ha: μ ≠ 12 B) H0: μ = 12 vs. Ha: μ > 12 C) H0: μ = 12 vs. Ha: μ < 12 D) H0: μ < 12 vs. Ha: μ = 12 12) A bottling company produces bottles that hold 10 ounces of liquid. Periodically, the company gets complaints that their bottles are not holding enough liquid. To test this claim, the bottling company randomly samples 22 bottles and finds the average amount of liquid held by the bottles is 9.7 ounces with a standard deviation of .4 ounce. Calculate the appropriate test statistic. A) t = -2.225 B) t = -3.437 C) t = -16.500 D) t = -3.518 13) A recipe submitted to a magazine by one of its subscribers states that the mean baking time for a cheesecake is 55 minutes. A test kitchen preparing the recipe before it is published in the magazine makes the cheesecake 10 times at different times of the day in different ovens. The following baking times (in minutes) are observed. 54 55 58 59 59 60 61 61 62 65 Assume that the baking times belong to a normal population. Test the null hypothesis that the mean baking time is 55 minutes against the alternative hypothesis μ > 55. Use α = .05.
Supreeta N.
A. ‐Carry out The Seven‐Steps Of Hypothesis Testing Procedures For Each Case‐ B. ‐Construct Proper Confidence Interval Of 95% For Each Case‐ 1. A sample of 9 high school seniors in a school system reports a mean of 5 hours worked at part‐time jobs during a recent week: The sample standard deviation was 3 hours. Do these data provide sufficient evidence to indicate that the mean for the population is less than 8 hours? Assume a normally distributed population. 2. The owner of the Ellenborough Shopping Center claims that more than 50% of the households within a three‐mile radius of the shopping center have at least one member who shops at the center at least once a week. In a sample of 300 households in the area, an investigator found that members of 171 households did so. Do these data provide sufficient evidence to support the shopping center owner's claim? Let ̑ =0.01. 3. A random sample of 16 college freshmen who plan to major in marketing and a random sample of 13 who plan to major in accounting are given a sales aptitude test. The variance of the scores of the marketing majors is 7.29. The variance of the scores of the accounting majors is 39.69. Do these data provide sufficient evidence to indicate, at the 0.05 level of significance, that the two population variances are different? State all necessary assumptions. 4. O'Connor Drugs, a pharmaceuticals manufacturer, is concerned with the side effects of a depressant drug when used by normal adults. A researcher would like to find a dosage that would produce sedation but not be strong enough to cause serious side effects. A random sample of 16 subjects taking part in an experiment with the drug achieved sedation with the following dosages, in milligrams per kilogram of body weight 1.6,1.8,7.3,5.7,3.0,1.6,3.8,3.1,7.8,7.4,4.2,1.6,2.1,2.1,5.5,4.4. Do these data provide sufficient evidence to indicate that the mean dosage required to produce sedation is greater‐than 2.5 milligram per kilogram of body weight? Let ̑ =0.05 5. An official with Bartram Paint and Varnish, Inc. believes that more than one‐third of ordered raw materials are not delivered on time. She compares the actual delivery date with the promised delivery date on a random sample of 100 orders. and finds that 38 orders were not delivered on time. Do these data support her belief? Let ̑ =0.01
Samriddhi S.
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