Crescent Oil has developed three new blends of gasoline – Blend X, Blend Y and Blend Z, and must decide which blend or blends to produce and distribute. A study of the miles per gallon ratings of the three blends is being conducted to determine if the mean ratings are the same for the three blends.

Five automobiles- 1, 2 3, 4 and 5, have been tested using each of the three gasoline blends and the miles per gallon ratings are shown on the accompanying Excel spreadsheet.

Based on the sample data we would like to determine whether the different blends of gasoline, produce significant differences in the average mpg. We would like to use the methods we have learnt so far in 361A to see if our result is statically significant. (Statistical significance refers to a result that is not likely to occur randomly but rather is likely to be attributable to a specific cause – in this case the different gasoline blends and different cars.)

Carry out the following tests and make preliminary findings:

1. For the sample data, calculate the means and standard deviations for the mpg for each of the three blends of gasoline – Blend X, Blend Y and Blend Z.
2. Draw three boxplots using Excel for mpg, one for each blend of gasoline.
3. Run three two sample t-tests between the different blends of gasoline i.e. compare the means of Blend X and Blend Y, then Blend X and Blend Z and finally Blend Y and Blend Z. Are they the same or are they different?
4. Armed with this information above determine whether or not your results show that the three different gasoline blends produce the same average mpg or not. Your answers should specifically site the information you re using to make your determination.
5. Re-run parts 1 - 4 above but this time your focus is on the mpg of each car for the 5 cars (car 1 through car 5) not for the three gasoline blends.

Your report should have the following sections, arranged sequentially:

1. Introduction and problem background

2. Data description and the business questions to be answered

3. Initial data exploration – descriptive statistics/graphs

4. Analyses

5. Interpretation of results, deficiencies in methods, final conclusions and recommendations for decision-making

An experiment was conducted to determine the effect of a high salt mean on the systolic blood pressure (SBP) of subjects. Blood pressure was determined in 12 subjects before and after ingestion of a test meal containing 10.0 gms of salt. The data obtained were:

1. Is a one-sided or two sided test needed here?
2. What is the mean SBP for each time period?
3. What is the standard deviation for each time period?
4. Which statistical test is appropriate to use on these data?
5. Carry out the hypothesis test(s) in question in above d. Use α=0.01
6. Are the means statistically different?
7. Find the 99% confidence interval for the difference of the two means on SBP. Interpret your finding                                                                                     

Media periodically discuss the issue of heights of winning presidential candidates and heights of their main opponents. The accompanying table lists the heights​ (cm) from several recent presidential elections. Construct a​ scatterplot, find the value of the linear correlation coefficient​ r, and find the​ P-value of r. Determine whether there is sufficient evidence to support a claim of linear correlation between the two variables. Should we expect that there would be a​ correlation? Use a significance level of alphaequals0.01

PRESIDENT: 180 177 194 170 181 178 195 178 172 187 190 187 178 194

OPPONENT: 180 176 184 171 178 184 176 183 180 181 168 182 189 175

1. The linear correlation coefficient r is __________. ​(Round to three decimal places as​ needed.)

2. Determine the null and alternative hypotheses. (Type integers or decimals. Do not​ round.)

H 0​: p ______ _______

H1: p ______ _______

3. The​ P-value is ________. ​(Round to three decimal places as​ needed.)

4. Because the​ P-value of the linear correlation coefficient is ▼ less than or equal to, greater than the significance​ level, there ▼ is, is not sufficient evidence to support the claim that there is a linear correlation between the heights of winning presidential candiates and the heights of their opponents.

5. Should we expect that there would be a​ correlation?

A. ​No, because presidential candidates are nominated for reasons other than height.

B. ​No, because height is the main reason presidential candidates are nominated.

C. ​Yes, because presidential candidates are nominated for reasons other than height.

D. ​Yes, because height is the main reason presidential candidates are nominated. Click to select your answer(s) and then click Check Answer.

You wish to test the following claim (HaHa) at a significance level of α=0.001 For the context of this problem, μd=μ2-μ1 where the first data set represents a pre-test and the second data set represents a post-test.

      Ho:μd=0
      Ha:μd>0

You believe the population of difference scores is normally distributed, but you do not know the standard deviation. You obtain pre-test and post-test samples for n=16 subjects. The average difference (post - pre) is ¯d=19.3 with a standard deviation of the differences of sd=28.6

What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =

What is the p-value for this sample? (Report answer accurate to four decimal places.)
p-value =

The p-value is...

• less than (or equal to) αα
• greater than αα

This test statistic leads to a decision to...

• reject the null
• accept the null
• fail to reject the null

As such, the final conclusion is that...

• There is sufficient evidence to warrant rejection of the claim that the mean difference of post-test from pre-test is greater than 0.
• There is not sufficient evidence to warrant rejection of the claim that the mean difference of post-test from pre-test is greater than 0.
• The sample data support the claim that the mean difference of post-test from pre-test is greater than 0.
• There is not sufficient sample evidence to support the claim that the mean difference of post-test from pre-test is greater than 0.

1. The results of a recent poll on the preference of shoppers regarding two products are shown below.

​

At 95% confidence, the margin of error is

2. The following information was obtained from independent random samples taken of two populations.
Assume normally distributed populations with equal variances.

The degrees of freedom for the t distribution are

3. ​ For a sample size of 30, changing from using the standard normal distribution to using the t distribution in a hypothesis test,

Find the range for the population mean value with 95% and 65% confidence intervals for each set of data. mean1=3.611, Standard Deviation1=0.02c m, n=24, Mean2=3.632, Standard Deviation2=0.06 cm, n2=17

Use the data and Excel to answer this question. It contains the United States Census Bureau’s estimates for World Population from 1950 to 2014. You will find a column of dates and a column of data on the World Population for these years. Generate the time variable t. Then run a regression with the Population data as a dependent variable and time as the dependent variable. Have Excel report the residuals.

(a) Based on the ANOVA table and t-statistics, does the regression appear significant?

(b) Calculate the Durbin-Watson Test statistic. Is there a serial correlation problem with the data? Explain.

(d) What affect might your answer in part (b) have on your conclusions in part (a)?

Can you please give detailed steps to do on excel?

Write an accurate concluding statement for the following hypothesis tests.

(a) You claim that the mean volume of all 12 ounce cans of Fizzy Pop is less than 12 ounces. After analyzing the data and performing a hypothesis test, you fail to reject the null hypothesis.

(b) Fizzy Pop claims that most 12 ounce cans of Fizzy Pop contain more than 12 ounces. After analyzing the data and performing a hypothesis test, you reject the null hypothesis.

(c) You claim that the average speed of cars going down a certain stretch of highway is 72 mph. After analyzing the data and performing a hypothesis test, you fail to reject the null hypothesis.

Could you please explain how you would find(estimate, not calculate) the 95% confidence interval for a set of categorical data. example: 30 students pick what their favorite food is

pizza=13

hamburgers=7

fries=5

icecream=5

3. Use data in BUSI1013 Credit Card Balance.xlsx to complete the following. You will need to use a statistical package such as StatTools or the Regression program within Excel’s Data Analysis Add-in to generate the estimated regression equation and the ANOVA etc. (12 points)
   
   1. What is the estimated regression equation using Account Balance as the dependent variable, and Income, Years of Education, as well as Size of Household as the independent variable?
   2. Comment on the goodness of fit of the model using the coefficient of determination.
   3. Conduct an F test with the critical value approach to see whether the overall model is significant. Use α = 0.01.
   4. Perform a t test with p-value approach for the significance of the Income variable. Use α = 0.05.
   5. Perform a t test with the p-value approach for the significance of the Size of Household variable. Use α = 0.05.
   6. Estimate the Account Balance of a customer who has an income of $62 thousand, 14 years of education, and a household size of 3.

How many distinct arrangements can be formed from all the letters of ʺstudentsʺ?

2. The data in BUSI1013 Credit Card Balance.xlsx is collected for building a regression model to predict credit card balance of retail banking customers in a Canadian bank. Use this data to perform a simple regression analysis between Account balance and Income (in thousands). (12 points)
   
   1. Develop a scatter diagram using Account Balance as the dependent variable y and Income as the independent variable x.
   2. Develop the estimated regression equation.
   3. Use the estimated regression equation to predict the Account Balance of a customer with Income of $58 thousands.
   4. Use the critical-value approach to perform an F test for the significance of the linear relationship between account balance and Income at the 0.05 level of significance.
   5. What percentage of the variability of Account Balance can be explained by its linear relationship with Income?
   6. Use the p-value approach to perform a t test for the significance of the linear relationship between Account Balance and Income at the 0.05 level of significance.

1 The monthly sales of mufflers follow the normal distribution with a mean of 1250 and a standard deviation of 255. The manufacturer would like to establish inventory levels such that there is only a 2% chance of running out of stock. Refer to the table in Appendix B.1.  

Where should the manufacturer set the inventory levels?

part B

1 The manufacturer of a laser printer reports the mean number of pages a cartridge will print before it needs replacing is 11,300. The distribution of pages printed per cartridge closely follows the normal probability distribution and the standard deviation is 680 pages. The manufacturer wants to provide guidelines to potential customers as to how long they can expect a cartridge to last. Refer to the table in Appendix B.1.  

How many pages should the manufacturer advertise for each cartridge if it wants to be correct 95 percent of the time? (Round z-value to 2 decimal places and the final answer to the nearest whole number.)

Pages           

Test whether p 1 greater than p 2. The sample data are x 1 equals 124​, n 1 equals 259​, x 2 equals 139​, and n 2 equals 305. Determine test statistic and P value

According to a government energy agency, the mean monthly household electricity bill in the United States in 2011 was $109.54. Assume the amounts are normally distributed with standard deviation $25.00. Use the TI-84 Plus calculator to answer the following.

(a) What proportion of bills are greater than $132?

(b) What proportion of bills are between $90 and $145?

(c) What is the probability that a randomly selected household had a monthly bill less than

$129? Round the answers to at least four decimal places.