Marketing estimates that a new instrument for the analysis of soil samples will be very successful, moderately successful, or unsuccessful, with probabilities 0.3, 0.6, and 0.1, respectively. The yearly revenue associated with a very successful, moderately successful, or unsuccessful product is $10 million, $5 million, and $1 million, respectively. Let the random variable X denote the yearly revenue of the product. Determine the mean and variance of the random variable

Marketing estimates that a new instrument for the analysis of soil samples will be very successful, moderately successful, or unsuccessful, with probabilities 0.3, 0.6, and 0.1, respectively. The yearly revenue associated with a very successful, moderately successful, or unsuccessful product is $10 million, $5 million, and $1 million, respectively. Let the random variable X denote the yearly revenue of the product. Determine the mean and variance of the random variable

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Summary statistics for returns on two stocks X and Y are listed below. Mean 2.85% 5.91% Stock X Stock Y Variance 0.005000 0.006000 The covariance of returns on stocks X and Y is 0.002800. Consider a portfolio of 30% stock X and 70% stock Y. What is the variance of portfolio returns? Please round your answer to six decimal places.
To study the effect of temperature on yield in a chemical process, five batches were produced at each of three temperature levels. The results follow. 50°C 60°C 70°C Treatments Error Temperature Source of Variation Total 35 25 36 40 29 29 31 33 = 22 25 Construct an analysis of variance table. (Round your values for MSE and F to two decimal places, and your p-value to four decimal places.) 22 = 27 28 31 37 Sum Degrees of Squares of Freedom O Ho: H50°C 60°C = #70°C Ha: H50°C H60°C # H70°C Use a 0.05 level of significance to test whether the temperature level has an effect on the mean yield of the process. State the null and alternative hypotheses. O Ho: H50°C 60°C = μ70°C Ha: Not all the population means are equal. Mean Square O Ho: At least two of the population means are equal. H: At least two of the population means are different. O Ho: H50°C 60°C # H70°C # Ha: H50°C 60°C = 70°C O Ho: Not all the population means are equal. F p-value
p value, t test and conclusion
To study the effect of temperature on yield in a chemical process, five batches were produced at each of three temperature levels. The results follow. Temperature 50°C 60°C 70°C 34 29 23 24 30 28 36 33 28 39 22 30 32 26 31 a. Construct an analysis of variance table (to 2 decimals but p-value to 4 decimals, if necessary). Source of Variation Sum of Squares Degrees of Freedom Mean Square p-value Treatments Error Total b. Use a .05 level of significance to test whether the temperature level has an effect on the mean yield of the process. Calculate the value of the test statistic (to 2 decimals). The p-value is - select your answer - What is your conclusion? - Select your answer - 00
The table below shows the number of hours per day 11 patients suffered from headaches before and after 7 weeks of soft tissue therapy. At a =0.01, is there enough evidence to conclude that soft tissue therapy helps patients suffer from headaches? Assume the samples are random and dependent, and the population is normally distributed. Complete parts (a) through (f). Patient Daily headache hours (before) 2.9 3.2 Daily headache hours (after) 1.7 3.6 2.2 reduce the length of time 1 2 3 4 5 7 8 3.8 2.5 3.5 2.2 1.2 2.9 4.3 9 10 11 e 1.8 3.3 3.8 3.4 1.8 4.4 1.8 1.1 1.1 1.4 (a) Identify the claim and state Ho and H The claim is "The therapy helps to reduce the length of time patients suffer from headaches." Let Ha be the hypothesized mean of the patients' daily headache hours before therapy minus their daily headache hours after it. State Ho and H. Choose the correct answer below. O A. Ho: Ha sd O B. Ho: Hg s0 H H >0 OC. Ho: Hg d O D. Ho: Ha20 OE. Ho Ho =d OF. Ho: Hgzd
Part d answer choices are : first blank , reject or fail to reject . Second blank is , is it is not
To study the effect of temperature on yield in a chemical process, five batches were produced at each of three temperature levels. The results follow. Temperature 50°C 60°C 70°C 37 35 29 27 36 34 39 39 34 42 28 36 35 32 37 Construct an analysis of variance table (to 2 decimals but p-value to 4 decimals, if necessary). Source of Variation Sum of Squares Degrees of Freedom Mean Square p-value Treatments Error Total Use a 0.05 level of significance to test whether the temperature level has an effect on the mean yield of the process. Calculate the value of the test statistic (to 2 decimals). The p-value is - Select your answer- What is your conclusion? Select your answer -
Find the t-test
A professor claims that exam scores for non-accounting majors are more variable than for accounting majors. Random samples of 29 non-accounting majors and 29 accounting majors are taken from a final exam. Test at the 1% level the null hypothesis that the two population variances are equal against the alternative that the true variance is higher for the non-accounting majors. Assume the populations are normally distributed. Non-Accounting Accounting H₁:0² = 0² H₁:0² > 0² C. H₂:0² = 0² H₁:0² #0² nx = 29 ny = 29 S The critical value is X 2 represented by Ho and the alternative hypothesis is represented by H₁. Choose the correct answer below. OB. Ho: 0²20² H₁:0² <0² = 1611.016 = 446.238 2 OD. H₂:0² = 0² o H₁:0² <0² The test statistic is F = 3.610. (Round to three decimal places as needed.) (Round to two decimal places as needed.)
The data below are from an independent-measures experiment comparing three different treatment conditions. Use an analysis of variance with an α=.05 to determine whether these data indicate any significant mean differences among the treatment conditions (there is no need to write the answer in APA style). Treatment 1 Treatment 2 Treatment 3 0 1 6 1 4 5 0 1 8 3 2 5
A scientist claims that pneumonia causes weight loss in mice. The table shows the weights (in grams) of six mice before infection and two days after infection. At a 0.05. is there enough evidence to support the scientist's claim? Assume the samples are random and dependent, and the population is normally distributed. Complete parts (a) through (e) below. Mouse Weight (before) Weight (after) 1 2 3 4 6 22.9 23.1 21.1 20.1 10.1 20.1 21.5 22.3 20.3 10.6 18.1 10.0 (a) Identify the claim and state H, and H.- What is the claim? OA. Weight gain causes pneumonia in mice. OB. Weight loss causes pneumonia in mice. OC. Pneumonia causes weight gain in mice. D. Pneumonia causes weight loss in mice. Let μ be the hypothesized mean of the difference in the weights (before-after). What are Ho and H₂? On ₂120 H₂: 0 OE H₂ =0 H₁₂ 14, 20 H₁₂14-0 OF. 16:1 sd >
A magazine claims that the mean amount spent by a customer at Burger Stop is greater than the mean amount spent by a customer at Fry World. The results for samples of customer transactions for the two fast food restaurants are shown below. a= 0.10, can you support the magazine's claim? Assume the population variances are equal. Assume the samples are random and independent, and the populations are normally distributed. Complete parts (a) through (e) below. Burger Stop Fry World Xy = $9.13 5 = $0.78 X2 = $8.50 S2= $0.68 n= 17 n =8 (a) Identify the claim and state Ho and H. Which is the correct claim below? O A. "The mean amount spent by a customer at Fry World is greater than the mean amount spent by a customer at Burger Stop." "The mean amount spent by a customer at Burger Stop is greater than the mean amount spent by a customer at Fry World." Oc. "The mean amount spent by a customer at Burger Stop is not equal to the mean amount spent by a customer at Fry World." O D. "The mean amount…