Stats Math

Math 10 MPS - Homework 10

1. A researcher wanted to study users of smart phones and see if there has been a change in customer preference over the last 7 months. 1000 smart phone users were asked what brand of phone they were using and the results will be compared to the actual percentages (market share) from April 2013. Using a significance level of 5%, conduct a Chi-square goodness of fit test to see if there has been a change in customer preference. Data from 7 months ago: 30% Samsung 20% Apple 50% Other Sample from now: 360 Samsung 180 Apple 460 Other

2. In a recent SurveyUSA poll, 500 Americans adults were asked if marijuana should be legalized. The results of the poll were cross tabulated as shown in the contingency tables below. Conduct two tests for independence to determine if opinion about legalization of marijuana is dependent on gender or age

3. People who are concerned about their health may prefer hot dogs that are low in salt and calories. The data contains data on the calories and sodium contained in each of 54 major hot dog brands. The hot dogs are classified by type: beef, poultry, and meat (mostly pork and beef, but up to 15% poultry meat). Minitab output is attached for two different hypothesis tests.

a. A test for a difference in calories due to hot dog type will be performed.

i. Design the test. ii. Fill in the missing information in the ANOVA table on the next page.

iii. Conduct the test with an overall confidence level of 5%, including pairwise comparisons.

b. A test for a difference in sodium due to hot dog type will be performed.

i. Design the test. ii. Fill in the missing information in the ANOVA table on the last page.

iii. Conduct the test with an overall confidence level of 5%, including pairwise comparisons.

Male Female

Should be Legal 123 90 Should Not be Legal 127 160

18-34 35-54 55+ Should be Legal 95 83 48 Should Not be Legal 65 126 83

One-way ANOVA: Calories versus Type Source DF SS MS F p-value Type ______ 17692 ________ ________ 0.000 Error ______ 28067 ________ Total ______ 45759 Individual 95% CIs For Mean Based on Pooled StDev Level N Mean StDev ---+---------+---------+---------+------ Beef 20 156.85 22.64 (------*------) Meat 17 158.71 25.24 (------*------) Poultry 17 118.76 22.55 (------*------) ---+---------+---------+---------+------ 112 128 144 160 Grouping Information Using Tukey Method Type N Mean Grouping Meat 17 158.71 A Beef 20 156.85 A Poultry 17 118.76 B Means that do not share a letter are significantly different.

One-way ANOVA: Sodium versus Type Source DF SS MS F p-value Type ______ 31739 ________ ________ 0.179 Error ______ 455249 ________ Total ______ 486988 Individual 95% CIs For Mean Based on Pooled StDev Level N Mean StDev +---------+---------+---------+--------- Beef 20 401.15 102.43 (---------*----------) Meat 17 418.53 93.87 (-----------*----------) Poultry 17 459.00 84.74 (-----------*----------) +---------+---------+---------+--------- 360 400 440 480 Grouping Information Using Tukey Method Type N Mean Grouping Poultry 17 459.00 A Meat 17 418.53 A Beef 20 401.15 A Means that do not share a letter are significantly different.