The Assignment is in the attached file
STAT 1000 Name: Summer 2021 Quiz 4 1. Victor Malm offers an SAT prep course to high school students, claiming that his course will raise total scores by an average of 200 points. To test this, you get a random sample of 12 high school students to take the SAT’s before and after taking Victor’s prep course. The difference column (after minus before) has mean equal to 230 points, with a sample standard deviation of 144 points. Perform a 2- tailed t-test for whether Victor Malm’s claim is reasonable given your data A. (2Pts) What are your hypotheses? B. (2Pts) What is the test statistic? C. (2Pts) Suppose the critical t-values (for 11 degrees of freedom) that leave 2.5% in each tail are t∗ = ±2.201. Do you reject the null hypothesis or not? 2. Researchers were interested in the recidivism among the prison inmates. The researchers questioned each individual in the survey to find out how many times the inmate had been convicted of a crime prior to the inmate’s current conviction. The researchers came up with the following table that shows the probability of X, the number of times previously convicted, X 0 1 2 3 Probability .25 .4 .25 .1 To test this claim, the researchers randomly sampled 100 inmates from Canadian prisons and found the following data, # of previous convictions 0 1 2 3 Frequency 30 35 25 10 A. (2Pts) What are your hypotheses? B. (2Pts) What is the test statistic? C. (2Pts) What is the appropriate degrees of freedom? D. (1Pt) If the p-value is greater than 0.05, what is your conclusion? 3. Researchers were interested in comparing the long-term psychological effects of being on a high-carbohydrate, low-fat diet (LF) versus a high-fat, low-carbohydrate diet (LC). A total of 106 overweight and obese participants were randomly assigned to one of these two energy-restricted diates. At Week 52, 32 LC dieters and 33 LF dieters remained. Mood was assessed using a total mood disturbance score (TMDS), where a lower score is associated with a less negative mood. The LC group has a sample mean x̄1= 47.3 and standard deviation s1= 28.3. The LF group has a sample mean x̄2 = 19.3 and standard deviation s2 = 25.8. To test if there is a difference in the TMDS at Week 52, A. (2Pts) What are the null and alternative hypotheses? B. (2Pts) Calculate the test statistic using the general two-sample t test procedure. C. (2Pts) Calculate the test statistic using the pooled two-sample t test procedure. D. (1Pt) If in both procedures, the p-value is less than 0.05, what is your conclusion? STAT 1000 Name: Summer 2021 Quiz 4 1. Victor Malm offers an SAT prep course to high school students, claiming that his course will raise total scores by an average of 200 points. To test this, you get a random sample of 12 high school students to take the SAT’s before and after taking Victor’s prep course. The difference column (after minus before) has mean equal to 230 points, with a sample standard deviation of 144 points. Perform a 2- tailed t-test for whether Victor Malm’s claim is reasonable given your data A. (2Pts) What are your hypotheses? B. (2Pts) What is the test statistic? C. (2Pts) Suppose the critical t-values (for 11 degrees of freedom) that leave 2.5% in each tail are t∗ = ±2.201. Do you reject the null hypothesis or not? 2. Researchers were interested in the recidivism among the prison inmates. The researchers questioned each individual in the survey to find out how many times the inmate had been convicted of a crime prior to the inmate’s current conviction. The researchers came up with the following table that shows the probability of X, the number of times previously convicted, X 0 1 2 3 Probability .25 .4 .25 .1 To test this claim, the researchers randomly sampled 100 inmates from Canadian prisons and found the following data, # of previous convictions 0 1 2 3 Frequency 30 35 25 10 A. (2Pts) What are your hypotheses? B. (2Pts) What is the test statistic? C. (2Pts) What is the appropriate degrees of freedom? D. (1Pt) If the p-value is greater than 0.05, what is your conclusion? 3. Researchers were interested in comparing the long-term psychological effects of being on a high-carbohydrate, low-fat diet (LF) versus a high-fat, low-carbohydrate diet (LC). A total of 106 overweight and obese participants were randomly assigned to one of these two energy-restricted diates. At Week 52, 32 LC dieters and 33 LF dieters remained. Mood was assessed using a total mood disturbance score (TMDS), where a lower score is associated with a less negative mood. The LC group has a sample mean x̄1= 47.3 and standard deviation s1= 28.3. The LF group has a sample mean x̄2 = 19.3 and standard deviation s2 = 25.8. To test if there is a difference in the TMDS at Week 52, A. (2Pts) What are the null and alternative hypotheses? B. (2Pts) Calculate the test statistic using the general two-sample t test procedure. C. (2Pts) Calculate the test statistic using the pooled two-sample t test procedure. D. (1Pt) If in both procedures, the p-value is less than 0.05, what is your conclusion?