Math & Music (Raw Data, Software Required): There is a lot of interest in the relationship between studying music and studying math. We will look at some sample data that investigates this relationship. Below are the Math SAT scores from 8 students who studied music through high school and 11 students who did not. Test the claim that students who study music in high school have a higher average Math SAT score than those who do not. Test this claim at the 0.05 significance level.

You should be able copy and paste the data directly into your software program.

(a) The claim is that the difference in population means is positive (μ1 − μ2 > 0). What type of test is this?

This is a right-tailed test.

This is a left-tailed test.

This is a two-tailed test.

(b) Use software to calculate the test statistic. Do not 'pool' the variance. This means you do not assume equal variances. Round your answer to 2 decimal places.

(c) Use software to get the P-value of the test statistic. Round to 4 decimal places.

(d) What is the conclusion regarding the null hypothesis?

reject H0

fail to reject H0

(e) Choose the appropriate concluding statement.

The data supports the claim that students who study music in high school have a higher average Math SAT score than those who do not.

There is not enough data to support the claim that students who study music in high school have a higher average Math SAT score than those who do not.

We reject the claim that students who study music in high school have a higher average Math SAT score than those who do not.

We have proven that students who study music in high school have a higher average Math SAT score than those who do not.

Math & Music (Raw Data, Software Required):
There is a lot of interest in the relationship between studying music and studying math. We will look at some sample data that investigates this relationship. Below are the Math SAT scores from 8 students who studied music through high school and 11 students who did not. Test the claim that students who study music in high school have a higher average Math SAT score than those who do not. Test this claim at the 0.05 significance level.

You should be able copy and paste the data directly into your software program.

(a) The claim is that the difference in population means is positive (μ₁ − μ₂ > 0). What type of test is this?

This is a right-tailed test.This is a two-tailed test.    This is a left-tailed test.

(b) Use software to calculate the test statistic. Do not 'pool' the variance. This means you do not assume equal variances.
Round your answer to 2 decimal places.

t =

(c) Use software to get the P-value of the test statistic. Round to 4 decimal places.
P-value =

(d) What is the conclusion regarding the null hypothesis?

reject H₀fail to reject H₀    

(e) Choose the appropriate concluding statement.

The data supports the claim that students who study music in high school have a higher average Math SAT score than those who do not.There is not enough data to support the claim that students who study music in high school have a higher average Math SAT score than those who do not.    We reject the claim that students who study music in high school have a higher average Math SAT score than those who do not.We have proven that students who study music in high school have a higher average Math SAT score than those who do not.

Math & Music (Raw Data, Software Required):
There is a lot of interest in the relationship between studying music and studying math. We will look at some sample data that investigates this relationship. Below are the Math SAT scores from 8 students who studied music through high school and 11 students who did not. Test the claim that students who study music in high school have a higher average Math SAT score than those who do not. Test this claim at the 0.05 significance level.

You should be able copy and paste the data directly into your software program.

(a) The claim is that the difference in population means is positive (μ₁ − μ₂ > 0). What type of test is this?

This is a two-tailed test.

This is a right-tailed test.    

This is a left-tailed test.

(b) Use software to calculate the test statistic. Do not 'pool' the variance. This means you do not assume equal variances.
Round your answer to 2 decimal places.

t = ?

(c) Use software to get the P-value of the test statistic. Round to 4 decimal places.
P-value = ?

(d) What is the conclusion regarding the null hypothesis?

reject H₀

fail to reject H₀    

(e) Choose the appropriate concluding statement.

The data supports the claim that students who study music in high school have a higher average Math SAT score than those who do not.

There is not enough data to support the claim that students who study music in high school have a higher average Math SAT score than those who do not.    

We reject the claim that students who study music in high school have a higher average Math SAT score than those who do not.

We have proven that students who study music in high school have a higher average Math SAT score than those who do not.

A researcher wishes to determine whether there is a relationship between the Campus at which SACAP students are based and their statistics anxiety level. The results of the subsequent survey are given in the following table:

Perform an appropriate hypothesis test at α = 0.01. If a significant result is obtained, determine the strength of the relationship. Show all four decision making steps.

(Exam question) A pizza store wants to estimate the quarterly sales based on the student population in town. The following data is obtained:

Calculate the regression line. Provide an interpretation of the intercept and slope coefficients. Also give a prediction of sales when the student population is 17 thousand.

It has been claimed that the best predictor of today’s weather is today’s weather. Suppose that in the town of Octapa, if it rained yesterday, then there is a 60% chance of rain today, and if it did not rain yesterday there is an 85% chance of no rain today.
a) Find the transition matrix describing the rain probabilities.
b) If it rained Monday, what is the probability it will rain on Wednesday?
c) If it did not rain Friday, what is the probability of rain on Monday?
d) Using the transition matrix from part a, find the steady-state vector. Use this to determine the probability that it will be raining at the end of time.

The Perfectly Competitive Market model assumes that firms can easily enter and leave the market (industry), and that each firm is a “price-taker”. Assume that you and your group members live in the same town(city),and are planning to grow tomatoes in your backyards during the summer. You are planning to sell the tomatoes in a farmers’ market in your hometown (city).

Explain whether or not it will be easy for you to enter and (later) leave this market.

Do you think that you will influence the market price for tomatoes in this market or not?

In other words, will you be “price-takers” or not?

Annual per capita consumption of milk is 21.6 gallons (Statistical Abstract of the United States: 2006). Being from the Midwest, you believe milk consumption is higher there and wish to support your opinion. A sample of 16 individuals from the midwestern town of Webster City showed a sample mean annual consumption of 24.1 gallons with a standard deviation of 4.8.

Compute the value of the test statistic. (Round to two decimal places)

What is the p-value? (Round to three decimal places).

At α=0.05, what is your conclusion?

PART 2: Instructions: Write three paragraphs to answer this question:

Suppose a sociologist at John Jay College is given a grant to study “whether there is a binge drinking problem on the campus (and in the dorms and nearby neighborhood) of Small Town College (STC). Describe three different data collection methods that the John Jay sociologist could use to gather evidence to determine whether or not STC has a serious “binge drinking problem” on its campus.For each data collection method, suggest the questions or issues that the sociologist would focus upon.

Suppose that your favorite restaurant serves the best ramen dishes in town . Since you eat there so often, you've observed the following :

the patrons are 40% male ,

the probability that the patron orders a tofu-based meal given that the patron is male is 30%,

while the probability that the order is tofu-based given the patron is female is 50%.

One night, you walk into the restaurant and see a tofu-based dish on one of the tables that is partially eaten ,but the customer has already left. What is the probability that the customer was female?