ONE SAMPLE t-test. ABOUT STATISTIS AND ATHpptx

DISUSSION

1. ONE SAMPLE T-TEST

2. What is one sample t-test? A one-sample t-test is a statistical procedure used to determine if there is a significant difference between the sample mean and a known or estimated population mean.

3. Examples Example 1: Do students in SGS have a systolic blood pressure that differs from the national average of 120? Example 2: Does a single-serving sized bag of peanut M&Ms weigh the claimed weight of 1.74oz?

4. When to use one sample t-test? You can use the test for continuous data . Your data should be a random sample from a normal population.

5. One Sample T Test Hypotheses Null hypothesis (H0): The population mean equals the hypothesized value (µ = H0). Alternative hypothesis (HA): The population mean does not equal the hypothesized value (µ ≠ H0).

6. If the p-value is less than your significance level (e.g., 0.05), you can reject the null hypothesis. The difference between the sample mean and the hypothesized value is statistically significant. Your sample provides strong enough evidence to conclude that the population mean does not equal the hypothesized value.

7. ASSUMPTIONS FOR ONE SAMPLE T-TEST: 1. The sampling distribution is normally distributed .. 2. Data are measured at least at the interval level. 3. Variances in these populations are roughly equal . 4. Scores are independent (because they come from different people).

8. QUESTION: An educator claims that the college student average IQ score is 115. A random sample of 30 student with IQ score is shown in Table 1. Is there enough evidence to reject the educator’s claim at  = 0.05? Assume the sample was normally distributed.

9. Solution (using traditional method) 1. Hypotheses H o :  = 115 (claim) H a :  ≠ 115

10. TEST STATISTICS

11. CRITICAL VALUE t critical = (from t-test table; d.f = n-1 = 29, two-tailed, )

12. DECISION Since the test value didn’t fall into critical region, we do not reject the H

13. CONCLUSION There is not enough evidence to reject the claim. In conclusion, we can say that the college student’s average IQ score is 115.

14. Using SPSS to analyze the data 1. To label the data, go to variable view and change the name into Students and IQ Score. For decimal, change into 0.

15. 2. Select the test variable “IQ Score” and set the test value = 115 because we are testing to see if the data have could really come from a population with mean of 115.

16. SPSS Output 1.0 SPSS Output 1.1

17. The output from the one sample t -test contains only two tables. The first table (SPSS Output 1.0) provides summary statistics for the experimental conditions. From this table, we can see that the number of students is 30 (column labeled N). The mean is 112.03, with standard deviation of 8.604. What’s more, the standard error of mean (standard deviation of the sampling distribution) is 1.571 ( ).

18. The second table of output (SPSS Output 1.1) contains the main test statistics. The t statistic is calculated by dividing the mean difference by the standard error of the sampling distribution of differences . The value of t is then assessed against the value of t you might expect to get by chance when you have certain degree of freedom. For one sample t -test, degrees of freedom are calculated by subtracting the number of samples . SPSS produces the exact significance value of t , and we are interested in whether this value is less than or greater than .05. In this case the two-tailed value of p is .069, which is greater than .05, and so we would have to conclude that there was no significant difference in mean of this sample . In terms of the experiment, we can conclude that the college student’s average IQ score is 115.

19. EXERCISE The Government claims that the car traveling pass your house average 55km/h, but you think they are actually traveling much faster. You borrowed a police radar gun and record the speed of the next twenty six cars that pass your house. 55 , 60, 65, 55, 65, 60, 55, 75, 65, 78, 90, 56, 88, 50, 42, 63, 66, 54, 53, 67, 52, 88, 54, 78, 68, 66