Question

A diet doctor claims that the average North American is more than 20 pounds overweight. To test his claim, a random sample of 20 North Americans was weighed, and the difference between their actual and ideal weights was calculated. The data are listed here. Do these data allow us to infer at the 5% significance level that the doctor’s claim is true? 16 23 18 41 22 18 23 19 22 15 18 35 16 15 17 19 23 15 16 26

Answer 1

Claim :

Average North American is more than 20 pounds overweight:

Hypothsied Mean : = 20

Null hypothesis :H_o : average North American overweight = 20 pounds;

Alternate Hypothesis :H_a : Average North American overweight >  20 pounds (Right Tailed test)

Given,

x : Difference between their actual and ideal weights of the sample

	x	x-	(x-)2
	16	-4.85	23.5225
	23	2.15	4.6225
	18	-2.85	8.1225
	41	20.15	406.0225
	22	1.15	1.3225
	18	-2.85	8.1225
	23	2.15	4.6225
	19	-1.85	3.4225
	22	1.15	1.3225
	15	-5.85	34.2225
	18	-2.85	8.1225
	35	14.15	200.2225
	16	-4.85	23.5225
	15	-5.85	34.2225
	17	-3.85	14.8225
	19	-1.85	3.4225
	23	2.15	4.6225
	15	-5.85	34.2225
	16	-4.85	23.5225
	26	5.15	26.5225
Total	417		868.55
Mean:	20.85

Sample mean :

Sample standard deviation : s

Hypothesied Mean :	20
Sample Mean :	20.85
Sample Standard Deviation : s	6.7612
Sample Size : n	20
Level of significance :	0.05
Degrees of Freedom : n-1	19

p-value for Right tailed test:

As P-Value i.e. is greater than Level of significance i.e (P-value:0.2903 > 0.05:Level of significance); Fail to Reject Null Hypothesis

Not enough evidence to reject that the average North American overweight = 20 pounds at 5% significance level

The data does not allow us to infer at the 5% significance level that doctor's calim is true.

p-value is computed using excel function :

T.DIST.RT function
Returns the right-tailed Student's t-distribution.
The t-distribution is used in the hypothesis testing of small sample data sets. Use this function in place of a table of critical values for the t-distribution.
Syntax
T.DIST.RT(x,deg_freedom)
The T.DIST.RT function syntax has the following arguments:
• X Required. The numeric value at which to evaluate the distribution.
• Deg_freedom Required. An integer indicating the number of degrees of freedom.