Question

For an Independent t-test, you can either:

1. Perform all calculations by typing in formulas to compute the needed components and answers
2. You can use the "Data: Data Analysis: t-test: Two Sample Assuming Equal Variances" procedure
   • Examples of this procedure can be found in your text, Excel Appendix 10.1, p. 459

For a Paired Differences t-test (dependent t-test), you can either

1. Perform all calculations by typing in formulas to compute the needed components and answer.
2. You can use the "Data: Data Analysis: t-test: Paired Two Sample for Means" procedure
   • Examples of this procedure can be found in your text, Excel Appendix
     Flc Home Develcper ePa Layour Fcrma taREvi Viw cp Pewer PivotTemewhat you wart to clo Share Comments aihr Normal Cop Insert Delete formst Check Cell Linked Cell Sort&&Tind & Furmalling-Tab oula B Weight Weight One Month on First Client Later Diet Center 151 200 169 179 144 129 148 199 172 168 137 221 345 301 173 274 158 205 170 189 149 135 151 200 169 179 144 229 358 305 174 A diet center claims that it has the most effective weight loss program in the region. Its advertisments say, "Participants will lose more than 5 pounds within a month." Thirty-five clients of this program weigned on the first day of the diet and then one month later. The data is presented to the left of this text. 1. Set up the hypotheses to test whether the mean weight loss one month later is significantly less than the weight on the first day. Compute the 95% Confidence Interval for each variable 2. Using the appropriate commands in Excel, find the value of the test statistic. Assume the populations variances are unknown but equal. 10 13 12 3. Interpret the p-value at a.05 4. Based on these results, write an APA statement expressing the results of this study Null: μ Alternative: H 16 19 18 20 19 20 21 149 246 297 267 194 153 251 300 269 Data Analysis: Statement expressing results: Startin Salaries website, Se-arches Laber Costs Diet center O lype here to search
     

Answer 1

1. H0: Mean weight loss one month is equal to weight on first day.

H1: Mean weight loss one month is less than to weight on first day.

2.Using Excel

Weight One Month later Weight On first day 151 200 169 179 144 129 148 199 172 168 137 221 345 301 173 274 191 149 246 297 267 199 241 221 190 241 187 186 158 205 170 189 149 135 151 200 169 179 144 229 358 305 174 289 194 153 251 300 269 197 244 229 195 250 197 194 t-Test: Two-Sample Assuming Unequal Variances Weight One Month later Weight On first day 208.8857143 2912.515966 35 Mean Variance Observations Hypothesized Mean Difference df t Stat P(T<t) one-tail t Critical one-tail P(T<-t) two-tail t Critical two-tail 202.0571429 2868.584874 35 0 68 0.531322988 0.298463173 1.667572281 0.596926346 1.995468931

Confidence Interval = x bar ± CONFIDENCE

To find out the confidence interval for the population mean, we will use the following formula:

Significance level Standard deviation of the population: Sample size: 0.05 53.5591717153.96773079 35 0.05 35 CONFIDENCE(E16,E17,E18) |17.87920592 CONFIDENCE(alpha, standard_dev, size)

We get the result below:

Significance level:	0.05	0.05
Standard deviation of the population:	53.55917171	53.96773079
Sample size:	35	35
confidence	17.74385259	17.87920592

Therefore, the 95% confidence interval for one month later is is 202.05±17.74 which is equal to the range 148.497 and 219.8

95% bconfidence interval for one month later is is 208.885±17.879 which is equal to the range 191.006 and 226.765

Test statistic is -0.531

P-value = 0.596 which is greater than 0.05 so do not reject the null hypothesis.

Hope this will be helpful. Thanks and God Bless You :)