For a binomial experiment, p = P(success) and q = P(failure) and n = number of trials. P(x) = (x) (p²) (gª-³) If n = 10, p = 0.2, q = 0.8,
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- Here is the full ques.A high school physics teacher wondered if his students in the senior class this year will be more likely to go into STEM majors than Social Science and Liberal Arts major. He asked each of his 50 students about their first choice for major on their college applications and conducted a Chi-square test for goodness of fit with an alpha level of .05 to see if the number of students choosing each category differs significantly. -20 - STEM -20 - Social Sciences -10 - Liberal arts What is the variable in this test? What type of variable is it, and what are the null and alternative hypothesis?A telemarketer is trying two different sales pitches to sell a carpetcleaning service. For Sales Pitch I, he contacted 175 people and 62 of these people bought the cleaning service. For Sales Pitch II, he contacted 154 people and 45 of these people bought the cleaning service. Does this indicate that there is any difference in the population proportions of the people who will buy the cleaning service, depending on which sales pitch he uses? Use α = 0.05.
- A researcher designed a study to test whether caffeine use enhanced performance time to run a 100 meter sprint. The participants (n=30) ran a 100 meter sprint before the consumption of caffeine on day 1 and then they ran another 100 meter sprint on the following day 2 after ingesting caffeine. The average time taken to run the 100 meter sprint on day 1 was (M1) and the average to run on day 2 after caffeine was (M2). The variance for this study was calculated to be (S2). Does caffeine use improve the running time in the 100 meter sprint (e.g., lower time)? Use all of the data provided to you below and test at an alpha of 0.05. M1 = 26.53M2 = 14.69S2 = 207.75n=30 a) state null and alternate hypothesis b) what is the critical value c) what is the obtained value d) conclusionFor the model: Y= Bo + B1X1 + B2X2 + B3X3 + B4X4 + ɛ If sample size is n=30, what is the degree of freedom for Error? 4 5 29 25Please solve for all and show all the work and process, Thank you