Researchers want to test whether an Indian child's school grades are influenced by his or her caste. They believe graders simply take 10 points off the score of a test written by a student belonging to a lower caste. In order to test this hypothesis, they obtain the scores of children of higher and lower castes, on a test on which children are generally believed to do equally well. In their sample, among the 45 children belonging to the higher castes, the average grade was 74, with a standard deviation of 12. Among the 41 children belonging to the lower castes, the average grade was 61, with a standard deviation of 11. (a) Test the hypothesis that the difference in the mean scores of children of higher castes and the children of lower castes is 10 points at 1% significance level. (b) Define a two-sided confidence interval for the difference in the means. (c) Assuming that the caste bias does not impact the variance of the grades, rerun your hypothesis. (d) Report your two-sided confidence interval for part c

From the U.S. Census Bureau’s American Community Survey in 2019 it was found that 33.13%of United States residents over the age of 25 had an educational attainment of a bachelor’sdegree or higher. In the District of Columbia, the percentage of residents over the age of 25 whohad attained a bachelor’s degree or higher was 59.67%. An investigator for the U.S. CensusBureau took a random sample of seven residents from the District of Columbia and asked themtheir highest educational degree they had obtained. a) Verify that the sample from the District of Columbia satisfies the conditions of thebinomial experiment. Write one sentence to check each requirement in context of theinvestigation.b) Assuming the sample from the District of Columbia is a binomial experiment, build theprobability distribution in a single table and include the table in your solutions. You maypresent this table horizontally or vertically and leave the probabilities unrounded. Thereare two possible ways to do this:  To…

The Bureau of Labor Statistics reports that the official unemployment rate for Black people was 10.4% and 4.7% for White people in February 2015. Select all correct answers for this question. O The samples of white and black people are independent. The explanatory variable is the unemployment rate. The response variable is the unemployment rate. The response variable is race.

It is believed that 11% of all Americans are left-handed. A college needs to know how many left-handed desks to place in the big lecture halls being constructed on its campus. In a random sample of 340 students from that college, whether or not a student was left-handed was recorded for each student. The college wants to know if the data provide enough evidence to show that students at this college have a different percentage of left- handers than the general American population? State the random variable, population parameter, and hypotheses. State the Type I and Type II errors in the context of this problem. a) The symbol for the random variable involved in this problem is ? ✓ The wording for the random variable in context is as follows: Select an answer b) The symbol for the parameter involved in this problem is The wording for the parameter in context is as follows: Select an answer c) Fill in the correct null and alternative hypotheses: Ho?? ✓ HA: ? ✓ ? ✓ d) A Type I error in the…

A researcher wanted to know if there was a correlation between the number of times a boxer incurred head injuries (traumatic encephalopathy) to depression scores reported by the same individuals. The data for 10 boxers (number of injuries and depression scores from 0-10 where 0 means no depression) is as follows: Number of brain injury  Depression Score  0 1 9 10 4 7 7 8 2 1 1 0 8 10 5 5 0 2 4 6   a. Use the four steps of hypothesis testing and calculate a Pearson correlation for the above data, starting with the hypotheses.b. Find critical value at an alpha level at α=.05, two tailed.c. Include the coefficient of determination with a sentence explaining the outcome of both calculations in APA format.d. Create a scatter plot by hand of the above data set.

It is believed that 11% of all Americans are left-handed. A college needs to know how many left-handed desks to place in the big lecture halls being constructed on its campus. In a random sample of 210 students from that college, whether or not a student was left-handed was recorded for each student. The college wants to know if the data provide enough evidence to show that students at this college have a different percentage of left-handers than the general American population? State the random variable, population parameter, and hypotheses. State the Type I and Type II errors in the context of this problem.a) The symbol for the random variable involved in this problem is               The wording for the random variable in context is as follows:          b) The symbol for the parameter involved in this problem is               The wording for the parameter in context is as follows:          c) Fill in the correct null and alternative hypotheses:     H0:H0:                    HA:HA:…

In a study about learning styles, researchers used a group of 64 elementary school students who volunteered to be part of the study. The researchers gave each student a pre-test and based upon the results, they divided them into 32 pairs of similarly scoring students. School administrators then randomly assigned one student from each pair to mathematics instruction online while the other student received in-person instruction in a traditional classroom. At the end of the year, all 64 students received a mathematics assessment, measured on a 100-point scale.   The researchers calculated the difference (in person −− online) in the mathematics assessment scores for each pair of students. The 32 differences had a mean of 15 and a standard deviation of 3.9 points.   Construct and interpret a 95% confidence interval for the mean difference (in person −− online) in the mathematics assessment scores for all pairs of students like these who learn math either face-to-face or online.

Researchers wondered if there was a difference between males and females in regard to some common annoyances. They asked a random sample of males and females, the following question: "Are you annoyed by people who repeatedly check their mobile phones while having an in-person conversation?" Among the 538 males surveyed, 182 responded "Yes"; among the 552 females surveyed, 209 responded "Yes." Does the evidence suggest a higher proportion of females are annoyed by this behavior? Complete parts (a) through (g) below. n,Pi (1-P1) 2 10 and n2P2 (1-P2) 2 10 - p. B. The samples are independent. C. The samples are dependent. D. The sample size is more than 5% of the population size for each sample. E. The sample size is less than 5% of the population size for each sample. F. The data come from a population that is normally distributed. (c) What are the null and alternative hypotheses? Let p, represent the population proportion of females who are annoyed by the behavior in question and P2…

It is believed that 11% of all Americans are left-handed. A college needs to know how many left-handed desks to place in the big lecture halls being constructed on its campus. In a random sample of 210 students from that college, whether or not a student was left-handed was recorded for each student. The college wants to know if the data provide enough evidence to show that students at this college have a higher percentage of left-handers than the general American population? State the random variable, population parameter, and hypotheses. State the Type I and Type II errors in the context of this problem.

In the NFL, Coaches can throw "challenge" flags if they believe officials have made an incorrect call on the field. Then, based upon further analysis, the call is either overturned (because the referees were incorrect) or upheld (referees were correct). In the first eight weeks of last NFL season, there were 316 challenges made, with 154 of those calls overturned. The NFL team owners used this data to begin a lawsuit that claimed referees were wrong more than 50% of the time in challenged situations. They want to perform statistical analysis before filing that lawsuit. For the following question, select the answer which correctly responds. 0.50