Hypothesis and T-test Analysis Problem Set - Statistics Project Example

Hypothesis and T-test Analysis Problem Set Lesson 22 Problems 1-4 1. Computing total scores for the algebra test from the item scores To compute the total scores for the algebra test from the item scores, we use the ‘compute function’ by going to the transform menu at the top of the data view screen then selecting ‘compute’. On the dialog box that pops up, we type total in the window labeled target variable and type sum(item1 to item 8) in the window labeled Numeric Expression. Clicking on the Ok button gives us the totals which are 8, 6, 5, 7, 4, and 6. 2. The study seeks to determine if a new teaching method, the Involvement Technique is effective in teaching algebra to first graders. With 8 questions and 2 options for the responses, then having random selection results into two correct responses. Therefore, for the new methodology to be considered effective, then the students need to have more than two correct responses. Therefore, the test value for the study is 2. 3. Conducting a one-sample T-test on the total scores To conduct a one-sample T-test on the total scores, we click on Analyze menu found at the top of the Data View window and select Compare Means and select One-Sample T-test at the dialog box then select total as test variable and indicate 2 as the Test Value and click Ok to produce the Output. From our analysis, this is our output: One-Sample Statistics N Mean Std. Deviation Std. Error Mean total 6 6.0000 1.41421 .57735 One-Sample Test Test Value = 2 t df Sig. (2-tailed) Mean Difference 95% Confidence Interval of the Difference Lower Upper total 6.928 5 .001 4.00000 2.5159 5.4841 From the two tables; a) Mean algebra score is 6 b) T-test Value is 6.928 c) P-value is 0.001 for the 2-tailed test and 0.0005 in the case of a one tailed test 4. Result Section based on the Analysis A one sample T-test was conducted on the total scores for algebra from the item scores to establish whether the Involvement Technique is effective in teaching algebra by evaluating whether the means were significantly different from 2. Since the one-tailed probability is considerably less than 0.05, we fail to accept the null hypothesis and conclude that that the method is effective in teaching algebra to first graders. Provided below is the histogram with the normal curve for the distribution of the totals. Lesson 23 Problems 1-5 1. Computing Scores to obtain a total index of Life Stress (ILS) at age 40& 60 To compute scores to obtain a total index of Life Stress (ILS) at age 40 & 60), we use the ‘compute function’ by going to the transform menu at the top of the data view screen then selecting ‘compute’. On the dialog box that pops up, we type total in the window labeled target variable and type sum all the items in the window labeled Numeric Expression. 2. To compute a paired-sample T-test to determine if overall life stress, on average, increases or decreases with age in the population To conduct a one-sample T-test on the total scores, we click on Analyze menu found at the top of the Data View window and select Compare Means and select Paired-Sample T-test at the dialog box then input our variables and click Ok to produce the Output. From our analysis, this is our output: Paired Samples Statistics Mean N Std. Deviation Std. Error Mean Pair 1 Stress_40 151.8444 45 14.48346 2.15907 Stress_60 136.8667 45 9.94896 1.48310 Paired Samples Correlations N Correlation Sig. Pair 1 Stress_40 & Stress_60 45 .037 .810 From the table, it is evident that while the mean for age 40 is 151.8444, that of age 60 is 136.8667which is lower hence we are justified to conclude that overall life stress decreases for working women with increase in age. 3. Creating a difference variable to show the changes in life stress from 40 years of age to 60 years of age for each woman and creating a histogram to show these changes graphically From the computations, our SPSS output is; Paired Samples Test Paired Differences t df Sig. (2-tailed) Mean Std. Deviation Std. Error Mean 95% Confidence Interval of the Difference Lower Upper Pair 1 Stress_40 - Stress_60 14.97778 17.26595 2.57386 9.79051 20.16504 5.819 44 .000 From the SPSS output, the two tailed p-value is 0.01 which is less than 0.05 thus we fail to accept null hypothesis and conclude that there is no significant correlation between the levels of stress between the two different ages. Below is a histogram showing graphical representation of the distribution of working women’s life stress at ages 40 & 60. 4. Conducting paired-samples t tests to evaluate whether occupational stress probably declines as women get older, while interpersonal life stress may increase or stay the same First we have to clearly outline the hypothesis under study; For occupational stress H0: Occupational stress does not decline as women get older H1: Occupational stress declines as women get older For interpersonal life stress H0: Interpersonal life stress levels do not increase or stay the same as women get older H1: Interpersonal life stress levels increase or stay the same as women get older Below is the SPSS output of the analysis; Interpersonal and Occupational Life Stress Scores for Women 40 & 60 Paired Samples Statistics Mean N Std. Deviation Std. Error Mean Pair 1 Interpersonal life stress at age 40 78.20 45 11.655 1.737 Interpersonal life stress at age 60 75.00 45 7.711 1.149 Pair 2 Occupational life stress at age 40 73.64 45 9.547 1.423 Occupational life stress at age 60 61.87 45 6.625 .988 From the results, the P-value is 0.13 which is greater than 0.05 hence we fail to reject the null hypothesis and conclude that interpersonal stress levels do not increase or stay the same as women get older. 5. A results section based on the analyses in Exercises 1-4 Interpersonal and Occupational Life Stress Scores for Working Women at Ages 40& 60 Paired Samples Test Paired Differences t df Sig. (2-tailed) Mean Std. Deviation Std. Error Mean 95% Confidence Interval of the Difference Lower Upper Pair 1 Interpersonal life stress at age 40 - Interpersonal life stress at age 60 3.200 13.942 2.078 -.989 7.389 1.540 44 .131 Pair 2 Occupational life stress at age 40 - Occupational life stress at age 60 11.778 12.696 1.893 7.964 15.592 6.223 44 .000 The study mainly aimed at establishing whether overall life stress increases or decreases as working women grow older. Consequently, from the results, it was evident that overall life stress index (ILS) at age 40 is 151.84 while at age 60 is 136.87. Consequently, the mean difference in overall stress between age 40 & 60 lies between 9.79 and 20.16. Read More