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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.
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- A second-stage smog alert has been called in a certain area of Los Angeles County in which there are 50 industrial firms. An inspector will visit 10 randomly selected firms to check for violations of regulations. a. If 15 of the firms are actually violating at least one regulation, what is the pmf of the number of firms visited by the inspector that are in violation of atleast one regulation? b. If there are 500 firms in the area, of which 150 are in violation, approximate the pmf of part (a) by simpler pmf. c. For X = the number among the 10 visited that are in violation, compute E(X) and V(X) both for the exact pmf and the approximating pmf in part (b).A research center claims that that 31% of adults in a certain country would travel into space on a commercial flight if they could afford it. In a random sample of 1200 adults in that country, 33% say that would travel into space on a commercial flight if they could afford it. At alpa= 0.05, isthere enough evidence to reject the research centers claim complete parts a through d belowA research center claims that 30% of adults in a certain country would travel into space on a commercial flight if they could afford it. In a random sample of 700 adults in that country, 34% say that they would travel into space on a commercial flight if they could afford it. At α=0.01, is there enough evidence to reject the research center's claim? Complete parts (a) through (d) below.
- A manufacturer of light bulbs may want to be reasonably certain that less than 3% of the bulbs are defective. Suppose 300 bulbs are randomly selected from a very large shipment. Each tested and 10 defective bulbs are found. Does this provide sufficient evidence for the manufacturer to conclude that the fraction defective in the entire shipment is less than 0.03? State the hypotheses:A polling organization has been hired to conduct a survey to determine the proportion of people who are likely to support an upcoming ballot initiative. To help determine the size of the sample required for the main poll, a preliminary poll of 20 people is taken that yields the results below. (Yes indicates that the person will support the initiative, No indicates that they won't.) YesYesNoNoNoYesYesYesYesYesYesNoNoYesYesNoYesYesNoNoYesNoYesNoYesYesYesYesYesYesNoYesYesYesNoNoYesNoNoNo Based on the results of the peliminary poll, how large a sample is required for the main poll, assuming that the main poll should have a margin of error of 3% and a confidence level of 97.8%. Sample Size =A survey of heads of households showed the percentage of those who asked for a raise and the percentage of those who asked for a raise and the percentage who got one. Accordig to the survey, of the men interviwed 16% asked for a raise, and of those men who asked for a raise, 65% recieved the raise. If a man is selected at random from the survey population of women, find the following probabilites. (To three decimal places) P(man asked for a raise) P(man recieved raise, given he asked for one) P(man asked for raise and recieved raise)
- A research center claims that more than 32% of employees in a certain country have changed jobs in the past three years. In a random sample of 360 people from that country, 126 have changed jobs in the past three years. At α=0.05, is there enough evidence to support the center's claim? Complete parts (a) through (e) belowA research center claims that 29% of adults in a certain country would travel into space on a commercial flight if they could afford it. In a random sample of 800 adults in that country, 31% say that they would travel into space on a commercial flight if they could afford it. At a=0.05, is there enough evidence to reject the research center's claim? Complete parts (a) through (d) below. (a) Identify the claim and state H0 and Ha. Identify the claim in this scenario. Select the correct choice below and fill in the answer box to complete your choice. (Type an integer or a decimal. Do not round.) A. The percentage of adults in the country who would travel into space on a commercial flight if they could afford it is not ______%. B. No more than ______% of adults in the country would travel into space on a commercial flight if they could afford it. C. ______% of adults in the country would travel into space on a commercial flight if they could afford it. D. At least ______% of…An education researcher claims that 57% of college students work year-round. In a random sample of 400 college students, 228 say they work year-round. At α=0.05, is there enough evidence to reject the researcher's claim? Identify the claim and state H0 and Ha
- The start-up Pluggr has developed a wi-fi controlled spark plug for use in electric vehicles. During their production process, they create spark plugs in large batches. A batch is sent out for sale if more than 95% of spark plugs pass a reliability test. Rather than test every spark plug in the batch, they only test sample n=400 from each batch. In batch #876-5309, of the 400 spark plugs tests, 392 of them passed the reliability test. Using this data, test the null hypothesis that H0: p=0.95 vs Ha: p>0.95 at the alpha=0.01 level. What is the p-value of this test, and what is your conclusion?. A research center claims that at least 23% of adults in a certain country think that their taxes will be audited. In a random sample of 900 adults in that country in a recent year, 19% say they are concerned that their taxes will be audited. At α=0.01, is there enough evidence to reject the center's claim? Complete parts (a) through (e) below. (a) Identify the claim and state H0 and Ha.A law enforcement agent hypothesizes that more than 25% of the drivers stopped on Saturday nights for speeding are under the influence of alcohol. A sample of 50 drivers were stopped for speeding on a Saturday night. 14 of the drivers in the sample were under the influence of alcohol. Use α = 0.05 to test the followinghypotheses: H0 : p ≤ 0.25 Ha : p > 0.25 Compute the test statistic.