SW318 Social Work Statistics Slide 1 Estimation Practice Problem – 1 This question asks about the best estimate of the mean for the population. Recall that estimation of mean requires the variable of interest to be ordinal or interval level variable and [educ] is an interval level variable. The best estimate of the true mean for population that the sample represents is the sample mean. Thus, all we need to know to answer this question is the mean of [educ] in this data set of the sample.

SW318 Social Work Statistics Slide 2 Estimation of Population Mean in SPSS (1) Recall that you could get the basic statistics such as mean, standard deviation, standard error of the mean using: Analyze > Descriptive Statistics > Descriptives…

SW318 Social Work Statistics Slide 3 Estimation of Population Mean in SPSS (2) After select and move the variable [educ] to the “Variable(s):” box, click on “Options…” button.

SW318 Social Work Statistics Slide 4 Estimation of Population Mean in SPSS (3) Second, click “Continue” in the “Descriptives: Options” dialog box. Then, click on “OK” in the Descriptives dialog box. First, make sure Mean, Kurtosis, and Skewness were selected in the “Descriptives: Options” dialog box.

SW318 Social Work Statistics Slide 5 Estimation of Population Mean in SPSS (4) The skewness of the distribution (-.514) was between -1 and +1, but the kurtosis of the distribution (1.899) fell outside the range from -1.0 to However, the Central Limit Theorem tells us that the sampling distribution of means will be normally distributed if the sample size is 50 or larger, even if the variable itself is not normally distributed. Since the number is our sample is 665, we can apply the Central Limit Theorem in this problem. True is the correct answer to the problem. The mean for "highest year of school completed" [educ] of the sample in the data set was The best estimate of the population is The SPSS output shows that the sample mean of [educ] is Recall that the best estimation of the population mean is the sample mean. Thus the best estimate of the population mean of [educ] is

SW318 Social Work Statistics Slide 6 Confidence Interval Practice Problem – 1 This question asks about the 99% of confidence interval for the population mean of [tvhours].

SW318 Social Work Statistics Slide 7 Confidence Interval in SPSS (1) To find the 99% of confidence interval of [tvhours], go to: Analyze > Descriptive Statistics > Explore…

SW318 Social Work Statistics Slide 8 Confidence Interval in SPSS (2) Then, click “Statistics…” button. In the “Explore” window, select and move [tvhours] to “Dependent List:” box.

SW318 Social Work Statistics Slide 9 Confidence Interval in SPSS (3) In the Explore: Statistics dialog box, make sure “Descriptives” was checked and type in the level of confidence, 99% in this case, into “Confidence Interval for Mean:” box. Click “Continue” to close the Explore Statistics dialog box. Then click “OK” to close the Explore dialog box.

SW318 Social Work Statistics Slide 10 Confidence Interval in SPSS (4) Before you get your answer and close the output window, you might want to check the distribution of this sample data set. In the SPSS output of “Explore”, Skewness and Kurtosis were provided. It shows that the [tvhours] in this sample was not normally distributed because both skewness (2.880) and kurtosis (13.374) were larger than 1. However, the Central Limit Theorem tells us that the sampling distribution of means will be normally distributed if the sample size is 50 or larger, even if the variable itself is not normally distributed. Since the number is our sample is 227, we can apply the Central Limit Theorem in this problem.

SW318 Social Work Statistics Slide 11 Confidence Interval in SPSS (5) The SPSS output shows that the lower bound of the 99% confidence interval was 2.79 and the upper bound of the 99% confidence interval was Thus, we can be 99% confident that the true population mean for [tvhours] is between 2.79 and The answer to the question is true.

SW318 Social Work Statistics Slide 12 Confidence Interval Practice Problem – 2 This question asks about the 99% of confidence interval for the mean of [tvhours]. Note that the estimation of the population mean requires that the variable be interval or ordinal. Since [rincom98] is ordinal, you could estimate the true mean of this variable. However, since not all data analysts agree with the convention of computing standard scores for ordinal variables, a caution will be added to any true findings.

SW318 Social Work Statistics Slide 13 Confidence Interval in SPSS (6) Click on “Dialog Recall” icon in the Icon Bar to redo the “Explore” for [rincome98].

SW318 Social Work Statistics Slide 14 Confidence Interval in SPSS (7) After select and move [rincome98] to “Dependent List:” box, click “Statistics…” button.

SW318 Social Work Statistics Slide 15 Confidence Interval in SPSS (8) Make sure the level of confidence is the value you want, 99% in this case and click “Continue” and “OK”.

SW318 Social Work Statistics Slide 16 Confidence Interval in SPSS (9) The SPSS output shows that The lower bound of the 99% confidence interval was The upper bound of the 99% confidence interval was Thus, we can be 99% confident that the actual mean for "income" is between and However, this findings should be taken with caution because [rincome98] is an ordinal level variable. True with caution is the correct answer.

SW318 Social Work Statistics Slide 17 Steps in solving estimation & confidence interval problems - 1 The following is a guide to the decision process for answering homework problems about estimation & confidence interval: Is the variable ordinal or interval level? Incorrect application of a statistic Yes No Compute the mean, skewness, and kurtosis for the data set.

SW318 Social Work Statistics Slide 18 Steps in solving estimation & confidence interval problems - 2 Yes No Assumption of normality satisfied? (skew, kurtosis between -1.0 and + 1.0) No Sample size 50+ so Central Limit Theorem applies? Incorrect application of a statistic Yes

SW318 Social Work Statistics Slide 19 Steps in solving estimation & confidence interval problems - 3 Is the variable ordinal level? Yes No Examine the sample mean as the best estimation of the true population mean and lower and upper bounds of the confidence interval of 95% or 99% confidence level. Statistical values for the estimation of the population mean and confidence interval correct? False Yes No True with caution True