XI. Application of These Theories

Connect face recognition theory to how this explains an educator's own biases.

Provide strategies or ways for educators to check their perceptions and face recognition biases when relating to students and parents, as well as when recalling information about students and a situation.

The admissions office at Huge U. believes the geographical distribution of entering students may be changing. over the last 30 years, 45% of the students have come from Midwestern states, 20% from the Southwest, 20% from the coasts, 5% from the South, and 10% from the Northwest. A sample of 250 students from this year's entering class includes 96 from the Midwest, 61 from the Southwest, 45 from the coasts, 17 from the South, and 31 from the Northwest. Does this indicate that the current entering class has a different geographical distribution?

A study was designed to investigate the effects of two​ variables, (1) a​ student's level of mathematical anxiety and​ (2) teaching​ method, on a​ student's achievement in a mathematics course. Students who had a low level of mathematical anxiety were taught using the traditional expository method. These students obtained a mean score of 380 with a standard deviation of 50 on a standardized test. Assuming no information concerning the shape of the distribution is​ known, what percentage of the students scored between 280 and 480?

a) at least 75%

b) 88.9%

c) approximately 95%

d) approximately 68%

This problem has 6 parts. This is part 1 of 6.

Freshman college students are often wary of the “freshman 15”, gaining 15 pounds during the first year of college.  A dietitian on a local college campus decided to collect data to see the validity of the “freshmen 15”.  She randomly samples 15 students and measures their weight at the beginning of their first year of college and then again at the end.  A summary of the data is below.

The dietitian claims, "on average, there is no difference in the students' weights before and after their freshman year." Select the pair of hypotheses that are appropriate for testing this claim.

This problem has 6 parts. This is part 1 of 6.

Freshman college students are often wary of the “freshman 15”, gaining 15 pounds during the first year of college.  A dietitian on a local college campus decided to collect data to see the validity of the “freshmen 15”.  She randomly samples 15 students and measures their weight at the beginning of their first year of college and then again at the end.  A summary of the data is below.

The dietitian claims, "on average, there is no difference in the students' weights before and after their freshman year." Select the pair of hypotheses that are appropriate for testing this claim.

The reading speed of second grade students is approximately normal, with a mean of 91 words per minute (wpm) and a standard deviation of 11.

A) What is the probability that a single randomly selected student will read more than 97 words per minute?

B) What is the probability that a random sample of 12 students will have a mean reading rate of more than 97 words per minute?

C) There is a 5% chance that the mean reading speed of a random sample of 97 second grade students will exceed what value? (Round to the nearest integer)

Respond to the following:

a. Explain what 15 square meters means.

b. Convert 15 square meters to square centimeters. Explain why your method makes sense.

c.Describe a misconception about area measurements such as 4 square inches that some students sometimes have.

d. Describe a misconception about converting 9 yards to feet that some students sometimes have, even if they know how yards and feet are related.

e. Students sometimes say, “area is length times width.” Explain why this statement is not fully accurate.

A statistics instructor believes that fewer than 20% of students at a local college attended the premiere showing of the latest Harry Potter movie. She surveys 84 of her students and finds that 11 of them attended the midnight showing. The Type I error is to conclude that the percent of students who attended is

1.           at least 20% when, in fact, it is less than 20%.
2.           20%, when, in fact, it is 20%.
3.            less than 20%, when, in fact, it is at least 20%.
4.           less than 20%, when, in fact, it is less than 20%.

Please explain your answer.

A local university reports that 3% of its students take their general education courses on a pass/fail basis. Assume that 50 students are registered for a general education course.

a. Define the random variable in words for this experiment.

b. What is the expected number of students who have registered on a pass/fail basis?

c. What is the probability that exactly 5 are registered on a pass/fail basis?

d. What is the probability that more than 3 are registered on a pass/fail basis?

e. What is the probability that less than 4 are registered on a pass/fail basis?