Dependent Sample T-Test Researchers were interested in studying whether seniors who participated in Silver Sneakers had...

Dependent Sample T-Test

Researchers were interested in studying whether seniors who participated in Silver Sneakers had a significant weight loss over a 10 week period. Given the above information, answer the questions below (assume a level of significance of .05).

State the null and alternate hypotheses.
What is the independent variable?
What is the dependent variable?
Complete the table below:

Paired Samples Statistics
		Mean	N	Std. Deviation	Std. Error Mean
Pair 1	preweight Weight before the diet (kg)	72.53	78	8.723	.988
	weight10weeks Weight after 10 weeks on the diet	68.681	78	8.9245	1.0105

	Beginning Weight in kg	Weight after 10 weeks in kg
Sample Size
Sample Mean
Sample Standard Deviation
Estimated Standard Error

Using the information below, answer the following questions:

What is the mean difference?
What was the t value and degrees of freedom?
What was the p value?
Draw a conclusion based on the hypotheses. Phrase it in terms of the original research questions, not just whether you accept or reject the null.

Paired Samples Test
			Paired Differences
			Mean		Std. Deviation		Std. Error Mean		95% Confidence Interval of the Difference
									Lower
Pair 1	Weight before the diet (kg) - Weight after 10 weeks on the diet		3.8449		2.5515		.2889		3.2696
Paired Samples Test
				Paired Differences		t		df		Sig. (2-tailed)
				95% Confidence Interval of the Difference
				Upper
Pair 1		Weight before the diet (kg) - weight10weeks Weight after 10 weeks on the diet		4.4201		13.309		77		.000

Expert Solution

Ho :   µd=   0
Ha :   µd >   0
................
Level of Significance ,    α =    0.05       claim:µd=0

sample size ,    n =    78

mean of sample 1,    x̅1=   72.530

mean of sample 2,    x̅2=   68.681

mean of difference ,    D̅ =    3.849
......................

std dev of difference , Sd =        2.5515

std error , SE = Sd / √n =    2.5515   / √   78   =   0.2889
......................

t-statistic = (D̅ - µd)/SE = ( 3.849 - 0 ) / 0.2889 = 13.323
.......................

Degree of freedom, DF= n - 1 = 77
...................

p-value = 0.0000 [excel function: =t.dist.rt(t-stat,df) ]
.......................

decision: p-value <α , Reject null hypothesis

conclusion: there is sufficient evidence to say that seniors who participated in Silver Sneakers had a significant weight loss over a 10 week period

please revert for doubt

orchestra answered 2 years ago

How to do a dependent sample t-test and find t-crit

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