When operating normally, a manufacturing process produces tablets for which the mean weight of the active ingredient is 5 grams, and the standard deviation is 0.025 gram. For a random sample of 12 tables the following weights of active ingredient (in grams) were found:

5.014.695.034.984.984.955.005.005.035.015.044.95

Without assuming that the population variance is known, test the null hypothesis that the population mean weight of active ingredient per tablet is 5 grams. Use a two-sided alternative and a 5% significance level. State any assumptions that you make.

The president of Amalgamated Retailers International, Sam Peterson, has asked for your assistance in studying the market penetration for the company's new cell phone. You are asked to determine if the market share is equal to the company's claim of 35%. You obtain a random sample of potential customers from the area. The sample indicates that 258 out of a total sample of 800 indicate they will purchase from Amalgamated

[a] Using a probability of error , test the hypothesis that the market share equals the company's claim of 35% versus the hypothesis that the market share is not equal to the company's claim.

[b] Using a probability of error , test the hypothesis that the market share equals the company's claim of 35% versus the hypothesis that the market share is less than the company's claim.

Examples:

If you are using the JMP Hypothesis Test Calculator with the "Raw Data" option, your display should look like the image below. ... Hypothesis Test on Mean ? Choose Type of Test Summary Statistics Oz-test Ot-test Count Choose Type of Alternative Hypothesis Population mean is not equal to hypothesized mean (two-tailed) Population mean is less than hypothesized mean (one-tailed) Population mean is greater than hypothesized mean (one-tailed) 45 50 55 Strength Test Inputs Statistic Value 52.1667 Hypothesized Mean Sample Average 50 Sample Standard Deviation 5.39427 Significance Level (alpha) _05 Sample Size 30 Reveal Decision Test Results Result Value Standard Error of the Mean 0.9849 t-score 2.2 t Critical Value(s] 1.6991 Observed Significance (p-value) 0.018 Reject Null Hypothesis If you are using Analyze > Distribution and selecting Test Mean, your submission should include this display. Summary Statistics Mean 52.166667 Std Dev 5.3942711 Std Err Mean 0.9848547 Upper 95% Mean 54.180921 Lower 95% Mean 50.152413 N 30 Test Mean Hypothesized Value 50 Actual Estimate 52.1667 DF 29 Std Dev 5.39427 t Test Test Statistic 2.2000 Prob > It 0.0359' Prob > t 0.0180* Prob et 0.9820 47 48 49 50 51 52If you are using the JMP Hypothesis Test Calculator with the "Summary Statistics" option, your display should look like one of the two below. You must include your inputs and outputs in the same image. Hypothesis Test on Proportion + Choose Type of Alternative Hypothesis Test Inputs Population proportion is not equal to hypothesized proportion (two-tailed) 61% Population proportion is less than hypothesized proportion (one-tailed) 60 Population proportion is greater than hypothesized proportion (one-tailed) 50 399% ount Reveal Decision 20 Success Failure Hypothesized Proportion 0.5 Number of Successes 61 Sample Size 100 Significance Level (alpha) 0.05 Test Results Result Value Estimated Proportion 0.61 Standard Error of Proportion 3.05 z Critical Values 1.6449 Test Statistic 2.2 Observed Significance (p-Value) 0.0139 Reject Null Hypothesis Hypothesis Test on Mean P P + THE Choose Type of Test Test Inputs Oz-test Hypothesized Mean 50 t-test Sample Average 52.167 Sample Standard Deviation 5.394 Choose type of alternative Hypothesis Sample Size 30 Population mean is not equal to hypothesized mean (two-tailed) Significance Level (alpha) 0.05 Population mean is less than hypothesized mean (one-tailed) Population mean is greater than hypothesized mean (one-tailed) v Test Results Result Value Reveal Decision Standard Error of the Mean 0.9848 t-score 2.2004 t Critical Values 1.6991 Observed Significance (p-value) 0.0179 Reject Null Hypothesis