use dependent samples t test. Set hypothesis so what formula will I use to solve
Five people who were convicted of speeding were ordered by the court to attend a workshop. A special device put into their cars kept records of their speeds for two weeks before and after the workshop. The maximum speeds for each person during the two weeks before and the two weeks after the workshop are shown below. Using a two-tailed test, determine whether the workshop worked in reducing their speed.
here are the scores for before 65,62,60,70,68 and after 58,55,56,66,60
hypothesis be Ho:md=0 and H1:md is not equal to 0
You are looking for reduced speeding.
I am assuming "md" indicates the mean of the difference.
Ho is correct by H1 should be md<0
Be sure you subtract in the correct way.
after - before = less than zero
Use the formula for the t-test for dependent samples (sometimes called matched pairs). It should be in your book. It really is too complicated to write out here.
To determine whether the workshop worked in reducing their speed, we can use a dependent samples t-test. This type of test is used when comparing the means of two related groups or sets of observations.
In this case, the two related groups are the speeds before and after the workshop for the five individuals. The null hypothesis (Ho) states that the mean difference in speeds (md) before and after the workshop is equal to zero, indicating no change in speeds. The alternative hypothesis (H1) states that the mean difference in speeds is not equal to zero, suggesting a change in speeds.
To use the dependent samples t-test, we need to calculate the mean difference, standard deviation of the differences, and the t-value. Here's how you can calculate it step by step:
Step 1: Calculate the differences between the before and after speeds for each individual:
Difference = After Speed - Before Speed
For the given data, the differences are:
-7, -7, -4, -4, -8
Step 2: Calculate the mean difference (md):
md = (sum of differences) / (number of differences)
For the given data, the sum of differences is -30, and there are 5 differences:
md = -30 / 5
md = -6
Step 3: Calculate the standard deviation of the differences (sd):
sd = sqrt((sum of squared differences) / (number of differences - 1))
For the given data, the sum of squared differences is 170, and there are 5 differences:
sd = sqrt(170 / 4)
sd = sqrt(42.5)
sd ≈ 6.5192
Step 4: Calculate the t-value:
t = (md - hypothesized mean difference) / (sd / sqrt(number of differences))
For the given data, the hypothesized mean difference is 0, and there are 5 differences:
t = (-6 - 0) / (6.5192 / sqrt(5))
t ≈ -2.1683
Step 5: Determine the critical value for the t-test. This depends on the significance level (alpha) and the degrees of freedom (df). For a two-tailed test with 4 degrees of freedom and a significance level of 0.05, the critical value is approximately ±2.776.
Step 6: Compare the t-value with the critical value. If the absolute value of the t-value is greater than the critical value, reject the null hypothesis. Otherwise, fail to reject the null hypothesis.
In this case, the absolute value of the t-value (-2.1683) is less than the critical value (2.776), so we fail to reject the null hypothesis. This means that there isn't sufficient evidence to conclude that the workshop had a significant effect in reducing their speed.
Please note that you can use statistical software or online calculators to simplify and automate these calculations.