Students are asked to rate their preference for one of four video games. The following table lists the observed preferences in a sample of 100 students. State whether to retain or reject the null hypothesis for a chi-square goodness-of-fit test given the following expected frequencies. (Assume alpha equal to 0.05.)

(a) expected frequencies: 70%, 10%, 10%, 10%, respectively

Retain the null hypothesis.Reject the null hypothesis.    

(b) expected frequencies: 25%, 25%, 25%, 25%, respectively

Retain the null hypothesis.Reject the null hypothesis.    

Suppose a college student at a university presents to a physician with symptoms of headaches, fever, and joint pain. Let A = {headaches, fever, and joint pain}, and suppose that the possible disease state of the patient can be partitioned into: B1 = normal, B2 = common cold, B3 = mumps. From clinical experience, the physician estimates P (AjBi ): P (AjB1) = 0.001, P (AjB2) = 0.70, P (AjB3) = 0.95. The physician, aware that some students have contracted the mumps, then estimates that for students at this university, P (B1) = 0.95, P (B2) = 0.025, and P (B3) = 0.025.

Given the previous symptoms, which of the disease states is most likely? Be sure to clearly show your work.

The Graduate Management Admission Test (GMAT) has scores from 100 to 900.

Scores are supposed to follow a Normal distribution with a mean of 500 and standard deviation of 150.

a. Suppose you earned a 800 on your GMAT test. From that information and the 68-95-99.7 Rule, where do you stand among all students who took the GMAT?

b.Suppose you earned a 450 on your GMAT test. Where do you stand among all students who took the GMAT?

c. Assuming the GMAT scores are nearly normal with N(500, 150), what proportion of GMAT scores falls between 400 and 700?

Cultured liver hepatocytes are convenient for studying both exocytosis and receptor-mediated, clathrin-dependent endocytosis. As part of an advanced laboratory in cell biology, students are required to perform mutation studies on cultured liver hepatocytes to generate data that supports the proposed mechanism of receptor-mediated, clathrin-dependent endocytosis. Liver hepatocytes are cultured, mutagenized, and screened for defective receptor-mediated endocytosis. In order to distinguish unique mutants from one another, the students must design a series of experiments to distinguish between mutants that have the following mutations:

a). Cellular adaptor proteins are mutated to be non-functional

b). Clathrin is mutated to be non-functional

c). Dynamin is mutated to be non-functional

You are to test if the average SAT score in the high school students of Ontario is greater than 495. You set the hypotheses as below:

H₀: µ = 495 vs Ha: µ > 495

If the SRS of 500 students were selected and the standard deviation has been known to 100, with alpha = 0.05, answer the followings.

a.  What is the Type I error?

b. What is the Type II error if the true population mean is 510. Explain it.

c. What is the power if the true population mean is 510? Explain it.

Please show your work and thank you SO much in advance! You are helping a struggling stats student SO much!

A non-profit program for youths sends students to summer camp. The price of the program is $800 per student, and there are 8 students that can participate in each program. Each program runs for 11 days. The price for all food and equipment is $100 per student per day. Also, the two program guides cost $150 a day to hire.

a. What is the profit margin for the program?

b.The non-profit was able to get a grant to cover $200 per student per day. Will this be enough to cover the full cost of the program?

c. Given the cost of the program, if the non-profit secured the grant, would you recommend they continue to operate the program based on the economics?

1. A sports scientist collects strength data from two groups of students. The first group is a group of athletes who might be expected to be strong, and the second group is a control group of nonathletic students. The first group has strength ratings of: c(129.4, 111.8, 127.7, 130, 120.7, 118.2, 121.9) And the second group has strength ratings of: c(149.1, 111.6, 122.1, 126.4, 123.3, 105.5, 127.3, 101.2, 113.3 ) Is there evidence that the first group is actually stronger than the second?

(a) State a sensible null hypothesis

(b) Is a one-sided or two-sided test needed? justify

(c) Perform a student t-test using R and interpret

1. Two students in a physics laboratory each have a concave mirror with the same radius of curvature, 52.0 cm. Each student places an object in front of a mirror. The image in both mirrors is two and a half times the size of the object. However, when the students compare notes, they find that the object distances are not the same. What is the distance of the farther object in cm?

I got 27.027 but that is incorrect

2. An object placed 27.0 cm in front of a convex mirror produces an image that is one-half the size of the object. What is the focal length of the mirror in cm ?(include the proper algebraic sign to reflect the nature of the mirror)

I got 34.01 but that is incorrect

In a recent survey of high school students, it was found that the amount of time spent on reading books per week was normally distributed with a mean of 32 minutes. Assume the distribution of weekly reading time follows the normal distribution with a population standard deviation of 2 minutes. Suppose we select a sample of 20 high school students.

a. What is the standard error of the mean time? Answer

b. What percent of the sample means will be greater than 32.50 minutes?  Answer

c. What percent of the sample means will be greater than 31.50 minutes?  Answer

d.    What percent of the sample means will be greater than 31.50 but less than 32.50 minutes? Answer

This financial option is offered by a university for its degree course that lasts exactly three years.

The students will repay in instalments after the end of the course. The instalments are determined as follows:

• No payments are made until three years after the end of the course.

• Over the following 15 years, students pay the university RM325 at the beginning of each quarter.

• After 15 years of payments, the quarterly instalments are increased to RM375 at the beginning of each quarter.

• After a further 15 years of payments, the quarterly instalments are increased to RM450 at the beginning of each quarter for a further 15-year period after which there are no more payments.

The rate of interest is at 3% per annum effective.

Calculate the present value.