Problem 3 In a (general) completely randomized design, show analytically that the sum of squares total (SST) is equal to the sum of two components: sum of squares due to treatments (SSTR), and sum of squares due to error (SSE).
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- How did you get the variance for this problem ?Find the variance of the random variable Z = 1−YResearchers wanted to test the hypothesis that living in the country is better for your lungs than living in a city. To eliminate the possible variation due to genetic dif- ferences, they located seven pairs of identical twins with one member of each twin living in the country, the other in a city. For each person, they measured the percentage of in- haled tracer particles remaining in the lungs after one hour: the higher the percentage, the less healthy the lungs. They found that for six of the seven twin pairs the one living in the country had healthier lungs. Based on the sample size and distance between the null value and the observed proportion, estimate the strength of evidence: inconclusive, weak but suggestive, moder- ately strong, strong, or overwhelming.
- You have been asked to determine the probability that the contribution margin for a particular product line exceeds the fixed cost of $1650. The total number of units sold is a normally distributed random variable with a mean of 300 and a variance of 400 X- N(300, 400). The selling price per unit is $12. The total number of units produced is a normally distributed random variable with a mean of 300 and a variance of 900 Y- N(300, 900). The variable production cost is $6 per unit. Production and sales have a positive correlation of 0.50. What is the probability that the contribution margin for the product line exceeds the fixed cost of $1650? |(Type an integer or decimal rounded to four decimal places as needed.)An antidepressant has historically been known to relieve depression for 65% of patients who use the drug. The drug's formula was changed recently to include smaller dose of its main, active ingredient. Due to this change, a medical researcher suspects that among all people with depression who use the new version of the drug, the proportion, p, of people who find relief is lower than 65%. A random sample of 240 patients who use the new version is selected by the researcher, and 149 of them find relief from depression. Based on these data, can we support the researcher's claim at the 0.05 level of significance? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.) (a) State the null hypothesis H and the alternative hypothesis H,. Ho :0 H¡ :0 (b) Determine the type of test statistic to use. (Choose one) ▼ OSO (c) Find the…An antidepressant has historically been known to relieve depression for 65% of patients who use the drug. The drug's formula was changed recently to include a smaller dose of its main, active ingredient. Due to this change, a medical researcher suspects that among all people with depression who use the new version of the drug, the proportion, p, of people who find relief is lower than 65%. A random sample of 215 patients who use the new version is selected by the researcher, and 125 of them find relief from depression. Based on these data, can we support the researcher's claim at the 0.05 level of significance? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.)
- An antidepressant has historically been known to relieve depression for 80% of patients who use the drug. The drug's formula was changed recently to include a smaller dose of its main, active ingredient. Due to this change, a medical researcher suspects that among all people with depression who use the new version of the drug, the proportion, p, of people who find relief is lower than 80%. A random sample of 215 patients who use the new version is selected by the researcher, and 159 of them find relief from depression. Based on these data, can we support the researcher's claim at the 0.05 level of significance? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.) (a) State the null hypothesis H and the alternative hypothesis H₁. H:0 H₁ :0 (b) Determine the type of test statistic to use. (Choose one) ▼ (c) Find the value…An antidepressant has historically been known to relieve depression for 80% of patients who use the drug. The drug's formula was changed recently to include a smaller dose of its main, active ingredient. Due to this change, a medical researcher suspects that among all people with depression who use the new version of the drug, the proportion, p, of people who find relief is lower than 80%. A random sample of 245 patients who use the new version is selected by the researcher, and 178 of them find relief from depression. Based on these data, can we support the researcher's claim at the 0.01 level of significance? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.) (a) State the null hypothesis H, and the alternative hypothesis H,. p H, :0 H :0 (b) Determine the type of test statistic to use. (Choose one) ▼ D=0 OSO (c)…Two samples are selected from a population, and a treatment is administered to the samples. If both samples have the same mean and the same variance, you are more likely to find a significant treatment effect with a sample of n = 100 than with a sample of n = 4. true or false?
- An antidepressant has historically been known to relieve depression for 65% of patients who use the drug. The drug's formula was changed recently to include a smaller dose of its main, active ingredient. Due to this change, a medical researcher suspects that among all people with depression who use the new version of the drug, the proportion, p, of people who find relief is lower than 65%. A random sample of 245 patients who use the new version is selected by the researcher, and 139 of them find relief from depression. Based on these data, can we support the researcher's claim at the 0.10 level of significance? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.) (a) State the null hypothesis Ho and the alternative hypothesis H₁. Ho :O H₁ :0 (b) Determine the type of test statistic to use. (Choose one) ▼ (c) Find the…When conducting a t-test for independent samples we have 2 ways of computing the variance. One way is to compute the variance for each sample, but this only works if the samples are the same size. If the samples are different sizes, we use a different equation. What is this variance equation that should be used if the two samples are not the same size?An antiaepressant has historically been known to relieve depression for 80% of patients who use the drug. The drug's formula was changed recently to include a smaller dose of its main, active ingredient. Due to this change, a medical researcher suspects that among all people with depression who use the new version of the drug, the proportion, p, of people who find relief is lower than 80%. A random sample of 175 patients who use the new version is selected by the researcher, and 135 of them find relief from depression. Based on these data, can we support the researcher's claim at the 0.10 level of significance? Perform a one-tailed test. Then complete the parts below. Carry your intermediate computations to three or more decimal places and round your answers as specified in the table. (If necessary, consult a list of formulas.) (a) State the null hypothesis H, and the alternative hypothesis H.. H, : (b) Determnine the type of test statistic to use. C=D ロS口 (Choose one) (c) Find the…
