Baseball Soccer 190 165 200 190 187 185 182 187 192 183 205 189 185 170 177 182 207 172 225 180 230 167 195 190 169 185 186 156 210 168 198 173 180 158 182 150 193 172 200 180 195 184 182 174 193 190 190 156 186 163 Female Male 8.2 9.5 9.3 9.9 8.5 8.3 8.6 8.8 8.7 8.5 8.1 7.9 8.3 8 7.9 8.7 8.6 8.3 9.5 8.9 10 10.4 9.7 9 9.6 10.8 9.2 9.5 8.9 8.9 9.1 9.6 9.4 10.6 9.5 10 8.8 9.5 9.3 9.4 Subject UCSB CSUN Algebra 76.35 112.5 Anthro 86 70.5 Art 25.95 83 Biology 115.28 88.75 Chem 128.35 140.25 Chicano 18.95 12 Commun 37.5 62.25 Econ 87.95 126 Educ 35.95 32 English 65.95 47 Geog 83 96.75 Geol 87.65 94.5 Health 29.95 56.5 History 29.95 48 Human 45 82 Japanese 45 95.75 Journalism 44.95 84.75 Music 29.95 30.25 Phil 60.3 66.25 Physics 106.65 137.75 PolySci 87.95 77.75 Soc 74.75 87 Theatre 24.95 33 Women 35.95 48.75 STATS 240 Class Section: # Lab Report #6 Student Name: XXXXXX Student ID: ####### Question 1: A random sample of male college baseball players and a random sample of male college soccer players were obtained independently and weighted. The distributions of both data sets suggest that the population distributions are roughly Normal. Test whether there is a significant difference between their mean weights, using a significance level of 10%. (a) State the null and alternative hypothesis. Also specify the type of test. Ho: Ha: (b) Insert the table \"Independent Samples Test\" (c) State the p-value from table from (b). Compare with the significance level (d) Make the conclusion. Explain whether we have strong evidence to support/reject the claim. Question 2: Brain size for 20 random women and 20 random men was obtained and is reported in the table (in hundreds of thousands of pixels shown in an MRI). Test the hypothesis that men tend to have larger brains than women at the 5% level. (a) State the null and alternative hypothesis. Also specify the type of test. Ho: Ha: (b) Insert the table \"Independent Samples Test\" (c) State the p-value from table from (b). Compare with the significance level (d) Make the conclusion. Explain whether we have strong evidence to support/reject the claim. Question 3: The prices of a sample of books at UCSB were obtained. Then the prices of books for the same subjects (at the same level) were obtained for CSUN. Assume that the distribution of differences is Normal enough to proceed, and assume that the sampling was random. Test the hypothesis that the population means are different, using a significance level of 5%. (a) State the null and alternative hypothesis. Also specify the type of test. Ho: Ha: (b) Insert the table \"Paired Samples Test\" (c) State the p-value from table from (b). Compare with the significance level (d) Make the conclusion. Explain whether we have strong evidence to support/reject the claim. STATS 240 Lab Spring 2016 Lab 6 Questions & Instructions NOTE: Send the lab report, SPSS output file, and copy & paste the lab report to stats240lab@gmail.com Subject of the submission e-mail: STATS240 (Class Section) Lab # Name Student ID LAB 6 Due Day: April 27th The purpose of Lab 6 is to use T-test to conduct a hypothesis test for two samples population means (both independent two sample test and paired two sample test). Guidelines for small sample inference for : Except in the case of small samples, the assumption that the data are a simple random sample (SRS) is more important than the assumption that the population is normally distributed. Always make a plot to check for skewness and outliers before you use the tprocedures. (For example, to check for outliers examine a boxplot.) Sample size less than 15. If the data are skewed or have outliers, do not use the tprocedures. (If you have to use it, be aware of the results. They may be biased.) Sample size from 15 to 40. The t-procedures can be used except in the presence of very strong skewness or outliers. Sample size greater than 40. The t-procedures can be used even for very skewed distributions when the sample size is large. 1. Instruction for two independent samples t test: STEP1: Enter the data into a column in the SPSS worksheet. Note: The data from both samples must be entered into a single column. In the second column, you have to indicate a name of each group. The variable format of the second column can be \"String.\" e.g. Var 1 100 350 175 150 100 Var 2 W W M M M STEP 2: Click on \"Analyze\" button on the tool bar; then go to \"Compare Means\" and then \"Independent-Samples T Test...\". Insert the 1st column's numerical data into \"Test Variables\". STEP 3: Insert the 2nd column's string data into \"Grouping Variables\". Then click on the \"Define Groups...\" button underneath. Then insert the group names you entered from Step 1. STEP 4: Click on the \"Options\" button, specify a confidence level alpha for a confidence interval for the difference between the true value of the population mean (the default confidence level is 95%) STEP 5: How to interpret the t-test result? 1. Read the \"sig.\" value from \"Levene's Test for Equality of Variances\" to check if the assumption of equal variances holds. 2(a). If the p-value of Levene's test is greater than 0.05, we can assume that the variance of two groups are the same and then read the two-sided p-value from the \"Equal variances assumed\" t-test . 2(b). If the p-value of Levene's test is less than 0.05, we have to use the \"Equal variances not assumed\" t-test result. Note: The t probability printed in the output corresponds to the P-value of a twosided test. If the value of the sample mean supports the alternative hypothesis, the Pvalue for a one-sided alternative is usually found by dividing this by 2. STEP 6: Insert the table \"Independent Samples Test\" from the output file to the lab report. Answer all questions listed in the lab report. Question 1: A random sample of male college baseball players and a random sample of male college soccer players were obtained independently and weighted. The distributions of both data sets suggest that the population distributions are roughly Normal. Test whether there is a significant difference between their mean weights, using a significance level of 10%. Question 2: Brain size for 20 random women and 20 random men was obtained and is reported in the table (in hundreds of thousands of pixels shown in an MRI). Test the hypothesis that men tend to have larger brains than women at the 5% level. 2. Instruction for two paired samples t test: STEP1: Enter the data into a column in the SPSS worksheet and rename the data appropriately. Note: For two paired samples, you will enter each group data into separate columns. STEP 2: Click on \"Analyze\" button on the tool bar; then go to \"Compare Means\" and then \"Paired-Samples T Test...\". STEP 3: Insert the first column sample data into \"Variable 1\" and insert the second column sample data into \"Variable 2\" STEP 4: Click on the \"Options\" button, specify a confidence level alpha for a confidence interval for the difference between the true value of the population mean (the default confidence level is 95%) Note: The t probability printed in the output corresponds to the P-value of a twosided test. If the value of the sample mean supports the alternative hypothesis, the Pvalue for a one-sided alternative is usually found by dividing this by 2. STEP 6: Insert the table \"Paired Samples Test\" from the output file to the lab report. Answer all questions listed in the lab report. Question 3 The prices of a sample of books at UCSB were obtained. Then the prices of books for the same subjects (at the same level) were obtained for CSUN. Assume that the distribution of differences is Normal enough to proceed, and assume that the sampling was random. Test the hypothesis that the population means are different, using a significance level of 5%