Answer each of the following questions by typing the answers into the Assignment text box below. For the predicted value of Y we will use Y-hat.

1. Sample data on exam grades (Y), hours studied (X₁) and homework average (X₂) was used to estimate the following regression equation: Y-hat = 60 + 5X₁ + .1 X_2.

The mean grade was 78.5. The standard error of estimate is Se = 5.25 and the coefficient of determination is R²=.873.

a. Interpret the standard error of the estimate.

b. Interpret the coefficient of determination.

c. Is this estimated regression equation a good fit? EXPLAIN.

Please show work.

Thanks

a)When is it appropriate to calculate a z-test?

b)What is the formula for a z-test?

c)If we set α = 0.10 what does that tell us?

d)If p < α then what should you do?

e)What is the z-table used for when conducting a z-test?

f)What are the 7 steps for hypothesis testing?

write a null alternative hypotheses that demonstrate an understanding of the guiding principles of ANOVA. explain how you came up with your answer.

A soda bottling plant fills cans labeled to contain 12 ounces of soda. The filling machine varies and does not fill each can with exactly 12 ounces. To determine if the filling machine needs adjustment, each day the quality control manager measures the amount of soda per can for a random sample of 50 cans. Experience shows that its filling machines have a known population standard deviation of 0.35 ounces.

In today's sample of 50 cans of soda, the sample average amount of soda per can is 12.1 ounces. Construct and interpret a 90% confidence interval estimate for the true population average amount of

soda contained in all cans filled today at this bottling plant. Use a 90% confidence level.
X =

population parameter:  =

Random Variable X=

Let x = age in years of a rural Quebec woman at the time of her first marriage. In the year 1941, the population variance of x was approximately σ² = 5.1. Suppose a recent study of age at first marriage for a random sample of 41 women in rural Quebec gave a sample variance s² = 2.9. Use a 5% level of significance to test the claim that the current variance is less than 5.1. Find a 90% confidence interval for the population variance.

(a) What is the level of significance?


State the null and alternate hypotheses.

H_o: σ² = 5.1; H₁: σ² > 5.1
H_o: σ² < 5.1; H₁: σ² = 5.1    
H_o: σ² = 5.1; H₁: σ² ≠ 5.1
H_o: σ² = 5.1; H₁: σ² < 5.1

(b) Find the value of the chi-square statistic for the sample. (Round your answer to two decimal places.)


What are the degrees of freedom?


What assumptions are you making about the original distribution?

We assume a exponential population distribution.
We assume a normal population distribution.    
We assume a uniform population distribution.
We assume a binomial population distribution.

(c) Find or estimate the P-value of the sample test statistic.

P-value > 0.100
0.050 < P-value < 0.100    
0.025 < P-value < 0.050
0.010 < P-value < 0.025
0.005 < P-value < 0.010
P-value < 0.005

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis?

Since the P-value > α, we fail to reject the null hypothesis.
Since the P-value > α, we reject the null hypothesis.    
Since the P-value ≤ α, we reject the null hypothesis.
Since the P-value ≤ α, we fail to reject the null hypothesis.

(e) Interpret your conclusion in the context of the application.

At the 5% level of significance, there is insufficient evidence to conclude that the variance of age at first marriage is less than 5.1.
At the 5% level of significance, there is sufficient evidence to conclude that the that the variance of age at first marriage is less than 5.1.    

(f) Find the requested confidence interval for the population variance. (Round your answers to two decimal places.)

Interpret the results in the context of the application.

We are 90% confident that σ² lies outside this interval.
We are 90% confident that σ² lies below this interval.    
We are 90% confident that σ² lies within this interval.
We are 90% confident that σ² lies above this interval.

7. It is widely accepted that people are a little taller in the morning than at night. Here we perform a test on how big the difference is. In a sample of 30adults, the morning height and evening height are given in millimeters (mm) in the table below. Use this data to test the claim that, on average, people are more than 10 mm taller in the morning than at night. Test this claim at the 0.01 significance level.

The age distribution of the Canadian population and the age distribution of a random sample of 455 residents in the Indian community of a village are shown below.

Age (years) Percent of Canadian Population Observed Number in the Village

Under 5 7.2% 42

5 to 14 13.6% 77

15 to 64 67.1% 288

65 and older 12.1% 48

Use a 5% level of significance to test the claim that the age distribution of the general Canadian population fits the age distribution of the residents of Red Lake Village.

(a) What is the level of significance?

State the null and alternate hypotheses.

H0: The distributions are different. H1: The distributions are different.

H0: The distributions are the same. H1: The distributions are the same.

H0: The distributions are the same. H1: The distributions are different.

H0: The distributions are different. H1: The distributions are the same.

(b) Find the value of the chi-square statistic for the sample. (Round your answer to three decimal places.)

Are all the expected frequencies greater than 5? Yes No

What sampling distribution will you use?

normal uniform chi-square binomial Student's t

What are the degrees of freedom?

(c) Estimate the P-value of the sample test statistic.

P-value > 0.100

0.050 < P-value < 0.100

0.025 < P-value < 0.050

0.010 < P-value < 0.025

0.005 < P-value < 0.010

P-value < 0.005

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis that the population fits the specified distribution of categories?

Since the P-value > α, we fail to reject the null hypothesis.

Since the P-value > α, we reject the null hypothesis.

Since the P-value ≤ α, we reject the null hypothesis.

Since the P-value ≤ α, we fail to reject the null hypothesis.

(e) Interpret your conclusion in the context of the application.

At the 5% level of significance, the evidence is insufficient to conclude that the village population does not fit the general Canadian population.

At the 5% level of significance, the evidence is sufficient to conclude that the village population does not fit the general Canadian population.

The following table shows ceremonial ranking and type of pottery sherd for a random sample of 434 sherds at an archaeological location.

Use a chi-square test to determine if ceremonial ranking and pottery type are independent at the 0.05 level of significance.

(a) What is the level of significance?


State the null and alternate hypotheses.

H₀: Ceremonial ranking and pottery type are not independent.
H₁: Ceremonial ranking and pottery type are independent.

H₀: Ceremonial ranking and pottery type are not independent.
H₁: Ceremonial ranking and pottery type are not independent.    

H₀: Ceremonial ranking and pottery type are independent.
H₁: Ceremonial ranking and pottery type are independent.

H₀: Ceremonial ranking and pottery type are independent.
H₁: Ceremonial ranking and pottery type are not independent.

(b) Find the value of the chi-square statistic for the sample. (Round the expected frequencies to at least three decimal places. Round the test statistic to three decimal places.)


Are all the expected frequencies greater than 5?

Yes No    

What sampling distribution will you use?

uniform
Student's t    
chi-square
normal
binomial

What are the degrees of freedom?


(c) Find or estimate the P-value of the sample test statistic. (Round your answer to three decimal places.)

p-value > 0.100
0.050 < p-value < 0.100    
0.025 < p-value < 0.050
0.010 < p-value < 0.025
0.005 < p-value < 0.010
p-value < 0.005

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis of independence?

Since the P-value > α, we fail to reject the null hypothesis.
Since the P-value > α, we reject the null hypothesis.    
Since the P-value ≤ α, we reject the null hypothesis.
Since the P-value ≤ α, we fail to reject the null hypothesis.

(e) Interpret your conclusion in the context of the application.

At the 5% level of significance, there is sufficient evidence to conclude that ceremonial ranking and pottery type are not independent.
At the 5% level of significance, there is insufficient evidence to conclude that ceremonial ranking and pottery type are not independent.    

Grades and AM/PM Section of Stats: There were two large sections of statistics this term at State College, an 8:00 (AM) section and a 1:30 (PM) section. The final grades for both sections are summarized in the contingency table below.

Observed Frequencies: O_i's

The Test: Test for a significant dependent relationship between grades and the section of the course. Conduct this test at the 0.05 significance level.(a) What is the null hypothesis for this test?

H₀: The section (AM/PM) of a course and the grades are independent variables.

H₀: The section (AM/PM) of a course and the grades are dependent variables.     

(b) What is the value of the test statistic? Round to 3 decimal places unless your software automatically rounds to 2 decimal places.

χ² = ?

(c) Use software to get the P-value of the test statistic. Round to 4 decimal places unless your software automatically rounds to 3 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.

We have proven that grades and section of the course are independent.

The evidence suggests that there is a significant dependent relationship between grades and the section of the course.    

There is not enough evidence to conclude that there is a significant dependent relationship between grades and the section of the course

 What are the different types of probability distribution and what are their characteristics?

probability 10%. n= 50 find between 15 and 18 times.

A small hypothetical study explored the response to two treatments where each subject in the study received both treatments (e.g. in a cross-over design). The data are given below 1) Analyze the information using a paired t-test (e.g. with GraphPad) a) What is the observed value of the test statistic from this test? b) What can you conclude about difference in mean response to the two treatments? Why?

A STAT 200 instructor believes that the average quiz score is a good predictor of final exam score. A random sample of 10 students produced the following data where x is the average quiz score and y is the final exam score.

x- 80, 95, 50, 60, 100, 55, 85, 70, 75, 85

y - 70, 96, 50, 63, 96, 60, 83, 60, 77, 87

(a) Find an equation of the least squares regression line. Round the slope and y-intercept value to two decimal places. Describe method for obtaining results. Show all work; writing the correct equation, without supporting work, will receive no credit. (b) Based on the equation from part (a), what is the predicted final exam score if the average quiz score is 65? Show all work and justify your answer. (c) Based on the equation from part (a), what is the predicted final exam score if the average quiz score is 40? Show all work and justify your answer. (d) Which predicted final exam score that you calculated for (b) and (c) do you think is closer to the true final exam score and why?