Consider a binomial experiment with two trials and p = 0.4. a. Draw a tree diagram for this experiment (see Figure 5.3). b. Compute the expected value, variance, and standard deviation
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Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
Consider a binomial experiment with two trials and p = 0.4.
a. Draw a tree diagram for this experiment (see Figure 5.3).
b. Compute the
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- 8- A random sample of the weight of 8 newborn babies at a local hospital is 6.5, 9.2, 8.5, 7.5, 6.7, 7.4, 8.2, and 7.1. Conduct a test of hypothesis to determine if the population mean is 7 pounds. (15%) b. Construct a 95% confidence interval for population standard deviation (6). Test if population variance (o) of the weight of newborns is equal to 0.25. Use a-0.10 and make sure to identify the null and the alternative, the test statistics, critical value(s), and the decision rule. d. What assumptions are needed for the validity of your answers in parts a, b, and c? a. с.The following three independent random samples are obtained from three normally distributed populations with equal variance. The dependent variable is starting hourly wage, and the groups are the types of position (internship, co-op, work study). Group 1: Internship Group 2: Co-op Group 3: Work Study 10.5 11 10.25 13.25 12.5 10.75 10 11.25 9.25 9.75 10.5 10.5 Use technology to conduct a one-factor ANOVA to determine if the group means are equal using a = 0.01. Group means (report to 2 decimal places): Group 1: Internship: Group 2: Co-op: Group 3: Work Study: 12.25 10.5 10.75 11.5 10 10.5 ANOVA summary statistics: F-ratio = (report accurate to 3 decimal places) p = (report accurate to 4 decimal places)An educational psychologist studies the effect of frequent testing on retention of class material. In one section of an introductory course, students are given quizzes each week. A second section of the same course receives only two tests during the semester. At the end of the semester, both sections receive the same final exam, and the scores are summarized below. Frequent Quizzes Two Exams n = 20 n = 20 M = 73 M = 68 A. If the first sample variance is s2 = 38 and the second sample has s2 = 42, do the data indicate that testing frequency has a significant effect on performance? Use a two- tailed test at the .05 level of significance. (Note: Because the two sample are the same size, the pooled variance is simply the average of the two sample variances.) tcritical…
- 2. Manufacturer A's television picture tubes have a mean lifespan of 7.13 years and a standard deviation of 0.8 years; while those of manufacturer B have a mean duration of 6.36 years and a standard deviation of 0.33 years. What is the probability that a random sample of 40 kinescopes from manufacturer A will have a mean lifespan that is 1 year longer than the mean lifespan in a sample of 45 kinescopes from manufacturer B? Round your answer to four decimal places after the period. Select one: a. The probability is 0.0469 b. The probability is 0.0464 c. None of the above d. The probability is 0.0455Suppose population 1 is all blue cars sold at used car auctions, and the mean sale price of all such blue cars is $24,579 with a standard deviation of $3,691. Additionally suppose population 2 is all red cars sold at used car auctions, and the mean sale price of all such red cars is $21,948 with a standard deviation of $4,028. If a simple random sample of 47 blue cars sold at used car auctions is selected and the mean sale price of the 47 blue cars in the sample is determined, and if an independent simple random sample of 59 red cars sold at used car auctions is selected and the mean sale price of the 59 red cars in the sample is determined, if appropriate describe completely the sampling distribution of X₁ - X₂ 1 Do we have 2 independent simple random samples? No YesThe following three independent random samples are obtained from three normally distributed populations with equal variance. The dependent variable is starting hourly wage, and the groups are the types of position (internship, co-op, work study). Group 1: Internship Group 2: Co-op Group 3: Work Study 10.75 12.5 8.5 9.75 10.25 12.5 11.5 13 15.25 10.75 14.25 14.5 11.25 10.5 14 10.5 11 15 13.75 12.75 11.75 11.5 12.5 15.75 11.75 12.75 12 13.25 13.75 14 12.75 14.25 12.25 Conduct a one-factor ANOVA to determine if the group means are equal using α=0.01α=0.01. Group means:Group 1 mean: Group 2 mean: Group 3 mean: ANOVA summary statistics:F-test statistic = p=p= Conclusion: The sample data suggests there is a correlation in the starting hourly wages. There is not sufficient data to conclude that at least one group's average starting hourly wage is different. The sample data suggests the starting hourly wages are dependent There is not…
- Suppose population 1 is all blue cars sold at used car auctions, and the mean sale price of all such blue cars is $24,579 with a standard deviation of $3,691. Additionally suppose population 2 is all red cars sold at used car auctions, and the mean sale price of all such red cars is $21,948 with a standard deviation of $4,028. If a simple random sample of 47 blue cars sold at used car auctions is selected and the mean sale price of the 47 blue cars in the sample is determined, and if an independent simple random sample of 59 red cars sold at used car auctions is selected and the mean sale price of the 59 red cars in the sample is determined, if appropriate describe completely the sampling distribution of X1 - X2? 8. What is the shape of the sampling distribution? Skewed Left Skewed Right Bimodal Normal 9. Are there any unusual features in this sampling distribution? Yes No4b.1Home work question:Please don't reject my probability question. (a) The first section entails selecting randomly 12 cans of peas from a canning factory's output on a given day, and weighing the contents. For the sample, the mean weight is 301-8 g, and the standard deviation is 1-8 g. Find the 99% confidence limits for the mean weight of peas in tins produced by the factory on the relevant day. Then, a second random sample of 12 tins is collected the following day. The mean and standard deviation of the contents for this sample are 302-1 gm and 1-6 gm, respectively. Show that a 95% confidence interval for the difference between the mean weights on the two days includes zero. Assuming that the variances of the weights are the same on the two days, do not change the variances of the weights.Assume right now that the samples taken on both days came from the same population. Based on the results of the two samples, calculate the 99% confidence interval for the population's mean tin…8
- Suppose a researcher pbserves a population of 12 people and computes SS=204. What is the variance? What is the standard deviation?4. Manufacturer A's television picture tubes have a mean lifespan of 7.23 years and a standard deviation of 0.72 years; while those of manufacturer B have a mean duration of 6.46 years and a standard deviation of 0.44 years. What is the probability that a random sample of 38 kinescopes from manufacturer A will have a mean lifespan that is 1 year less than the mean lifespan in a sample of 42 kinescopes from manufacturer B? Round your answer to four decimal places after the period.The following three independent random samples are obtained from three normally distributed populations with equal variance. The dependent variable is starting hourly wage, and the groups are the types of position (internship, co-op, work study). Group 2: Co-op Group 3: Work Study Group 1: Internship 10 10.5 11.25 11 9.25 10.25 9.75 13.25 10.5 12.5 10.5 10.75 Use technology to conduct a one-factor ANOVA to determine if the group means are equal using a = 0.01. Group means (report to 2 decimal places): Group 1: Internship: Group 2: Co-op: Group 3: Work Study: ANOVA summary statistics: F-ratio = (report accurate to 3 decimal places) 12.25 10.5 10.75 11.5 10 10.5 р (report accurate to 4 decimal places) Conclusion: © The sample data suggest the average starting hourly wages are not the same. O There is not sufficient data to conclude the starting wages are different for the different groups.
