Marketing estimates that a new instrument for the analysis of soil samples will be very successful, moderately successful, or unsuccessful, with probabilities 0.30, 0.56, and 0.14, respectively. The yearly revenue associated with a very successful, moderately successful, or unsuccessful product is $16 million dollars, $8 million dollars, and $1 million dollars, respectively. Let the random variableX denote the yearly revenue of the product in millions of dollars. Evaluate the cumulative distribution function of X at specified values. Round your answers to two decimal places (e.g. 98.76). F(1) = i F(8) = i F(16) = i
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- Hint(s) Check My Work The following data are from a completely randomized design. Treatment A B C 162 142 126 142 156 122 165 124 138 145 142 140 148 136 150 174 152 128 Sample mean 156 142 134 Sample variance 164.4 131.2 110.4 a. Compute the sum of squares between treatments (to the nearest whole number). b. Compute the mean square between treatments (to 1 decimal). c. Compute the sum of squares due to error (to the nearest whole number).A video game developer is testing a new game on three different groups. Each group represents a different target market for the game. The developer collects scores from a random sample from each group. Assume that the data are from normally-shaped distributions which have equal variances. The results are shown in the table below. Round all answers to 4 decimal places. Group A 105 101 103 104 109 Group B Group C 149 173 156 149 124 124 a. What is the F Statistic? b. What is the p-value? 190 194 102 102A new vaccination is being used in a laboratory experiment to investigate whether it is effective. There are 311 subjects in the study. Is there sufficient evidence to determine if vaccination and disease status are related? Vaccination Status Diseased Not Diseased Total Vaccinated 66 31 97 Not Vaccinated 69 145 214 Total 135 176 311 Copy Data Step 3 of 8: Find the expected value for the number of subjects who are vaccinated and are not diseased. Round your answer to one decimal place. E Tables E Keypad Answer How to enter your answer Keyboard Shortcuts Previous Step Answers Evaccinated and not diseased
- An automotive center keeps track of customer complaints received each week. The probability distributions of complaints are shown below. The random variable, xi, represents the number of complaints, and p(xi) is the probability of receiving xi complaints for two of the stores. The cost impact of each complaint is believed to be y=$10x3 where x is the number of complaints. Store A xi 0 1 2 3 4 5 6 p(xi) 0.10 0.15 0.20 0.25 0.15 0.10 0.05 Store B xi 0 1 2 3 4 5 6 p(xi) 0.10 0.15 0.25 0.22 0.13 0.08 0.07 Sample from these distributions to compute the total number of complaints (store A+B) per week for 52 weeks.Treatment Sham Researchers conducted a study to determine whether magnets are effective in treating back pain. The results are shown in the table for the treatment (with magnets) group and the sham (or placebo) group. The results are a measure of reduction in back pain. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard H1 H2 23 23 deviations are equal. Complete parts (a) and (b) below. 0.57 0.39 0.62 1.29 a. Use a 0.05 significance level to test the claim that those treated with magnets have a greater mean reduction in pain than those given a sham treatment. What are the null and alternative hypotheses? O A. Ho: H1 =H2 O B. Ho: H1 H2 H1: H1Test the claim that the samples come from populations with the same mean. Assume that the populations are normally distributed with the same variance. At the 0.025 significance level, test the claim that the four brands have the same mean if the following sample results have been obtained. Brand A Brand B Brand C Brand D 21 24 22 17 20 21 18 25 27 29 35 18 23 25 22 25 26 29 29 21 26 36 37Treatment Placebo A study was done using a treatment group and a placebo group. The results are shown in the table. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below. Use a 0.10 significance level for both parts. H1 H2 In 34 31 2.39 2.68 S 0.62 0.98 a. Test the claim that the two samples are from populations with the same mean. What are the null and alternative hypotheses? O B. Ho: H1 H2 OC. Ho: H1 =H2 O D. Ho: H1 H2 H1: H1The management of Brinkley Corporation is interested in using simulation to estimate the profit per unit for a new product. The selling price for the product will be $45 per unit. Probability distributions for the purchase cost, the labor cost, and the transportation cost are estimated as follows: Procurement Cost ($) Probability Labor Cost ($) Probability Transportation Cost ($) Probability 10 0.25 20 0.10 3 0.75 11 0.45 22 0.25 5 0.25 12 0.30 24 0.35 25 0.30 Compute profit per unit for the base-case, worst-case, and best-case scenarios. Construct a simulation model to estimate the mean profit per unit. Why is the simulation approach to risk analysis preferable to generating a variety of what-if scenarios? Management believes the project may not be sustainable if the profit per unit is less than $5. Use simulation to estimate the probability the profit per unit will be less than $5.According to Benford's Law, a variety of different data sets include numbers with leading (first) digits that follow the distribution shown in the table below. Test forgoodness-of-fit with Benford's Law. Leading Digit 1 2 3 4 5 6 7 8 9 Benford's law: distribution of leading digits 30.1% 17.6% 12.5% 9.7% 7.9% 6.7% 5.8% 5.1% 4.6% When working for the Brooklyn District Attorney, investigator Robert Burton analyzed the leading digits of the amounts from 784 checks issued by seven suspect companies. The frequencies were found to be 0, 12, 0, 73, 482, 186, 8, 23, and 0, and those digits correspond to the leading digits of 1, 2, 3, 4, 5, 6, 7, 8, and 9, respectively. If the observed frequencies are substantially different from the frequencies expected with Benford's Law, the check amounts appear to result from fraud. Use a 0.05 significance level to test for goodness-of-fit with Benford's Law. What is the value…Part 2 Let x be a random variable that represents the batting average of a professional baseball player. Let y be a random variable that represents the percentage of strikeouts of a professional baseball player. A random sample of n = 6 professional baseball players gave the following information. x 0.338 0.306 0.340 0.248 0.367 0.269 y 3.5 7.7 4.0 8.6 3.1 11.1 Σx = 1.868, Σy = 38, Σx2 = 0.592034, Σy2 = 294.32, Σxy = 11.1556, and r ≈ -0.901. Se ≈ 1.5890, a ≈ 26.420, and b ≈ -64.517. (a) Find the predicted percentage of strikeouts for a player with an x = 0.328 batting average. (Use 2 decimal places.) %(b) Find a 90% confidence interval for y when x = 0.328. (Use 2 decimal places.) lower limit % upper limit %Chocolate Chip Cookie Calories The average 1-ounce chocolate chip cookie contains 110 calories. A random sample of 14 different brands of 1-ounce chocolate chip cookies resulted in the following calorie amounts. At the a=0.10 level, is there sufficient evidence that the average calorie content is greater than 110 calories? Assume the population is normally distributed.100 105 185 105 110 115 150 120 180 120 150 100 125 151 a. State the hypotheses and identify the claim H0= (claim or not claim) H1= (claim or not claim) This hypothesis test is a (one tailed or two tailed) test Critical value(s)= t= (Reject or do not reject) the null hypothesis is there enough evidence to support the claim?Marketing estimates that a new instrument for the analysis of soil samples will be very successful, moderately successful, or unsuccessful, with probabilities 0.35,0.50, and 0.15, respectively. The yearly revenue associated with a very successful, moderately successful, or unsuccessful product is $6 mnillion dollars, $3 million dollars, and $1 million dollars, respectively. Let the random variableX denote the yearly revenue of the product in millions of dollars. Evaluate the cumulative distribution function of X at specified values. Round your answers to two decimal places (e.g. 98.76). 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