Question

A weight control program was being tested to determine whether it was truly effective. The participants were weighed before the program and after. Does the data below provide evidence at the 5% level that this program is effective?

15 A weight control program was being tested to determine whether it was truly effective. The participants were weighed before the program and after. Does the data below provide evidence at the 5% level that this program is effective? Participant before after difference Participant before after difference | 178 150 307 303 145 143 16 298 280 205 190 17 156 130 177 178 | 18 340 337 215 195 19 167 155 189 180 230 220 170 166 21 218 220 190 181 215 295 293 23 320 300 10 300 275 24 183 170 234 225 435 405 250 230 26 280 265 196 186 27 214 198 200 200 28 360 341 20 122 9 25 a. Make a histogram of the differences (before-after) and describe the distribution. Make this on a spreadsheet and remember to label the axes and give a title to the graph. b. Are there any outliers? Justify your answer. c. Does the data provide evidence (at the 5% level) that the program is effective? Give all the steps for your significance test. d. Why are parts a and b important for part c?

Answer 1

b) There is NO outliers.

c) (1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: μD​ = 0

Ha: μD​ > 0

This corresponds to a right-tailed test, for which a t-test for two paired samples be used.

(2) Rejection Region

Based on the information provided, the significance level is α=0.05, and the degrees of freedom are df=27.

Hence, it is found that the critical value for this right-tailed test is tc​=1.703, for α=0.05 and df=27.

The rejection region for this right-tailed test is R=t:t>1.703.

(3) Test Statistics

The t-statistic is computed as shown in the following formula:

(4) Decision about the null hypothesis

Since it is observed that t=7.33>tc=1.703, it is then concluded that the null hypothesis is rejected.

Using the P-value approach: The p-value is p=0, and since p=0<0.05, it is concluded that the null hypothesis is rejected.

(5) Conclusion:It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that population mean μ1 is greater than μ2, at the 0.05 significance level.

c) (a) and (b) are necessary to carry out t test.