Question

Question 4 (1 point) In a study to determine whether counseling could help people lose weight, a sample of people experienced a group-based behavioral intervention, which involved weekly meetings with a trained interventionist for a period of six months. The following data are the numbers of pounds lost for 5 people 18.2, 3.9, 17.1. 8.8. 7.7 It is reasonable to assume that the population is approximately normal. A researcher wants to know whether the mean weight loss is greater than 10 pounds. Compute the p-value of the test. Write down your P-value. You will need it for the next question. Write only a number as your answer. Round to four decimal places (for example: 0.3841). Your Answer:

Answer 1

Step 1:

Ho : $\mu$ = 10

Ha:  $\mu$ > 10

Null hypothesis states that mean weight loss is 10 pounds.

Alternative hypothesis states that the mean weight loss is greater than 10 pounds.

Step 2 : Test statistics

n = 5

Sample mean = sum of terms / no of terms = 55.5 /5 = 11.14

Samle standard deviation = s

S Στί – i))2 η -1 = I V

data	data-mean	(data - mean)2
18.20	7.06	49.8436
3.90	-7.24	52.4176
17.10	5.96	35.5216
8.80	-2.34	5.4756
7.70	-3.44	11.8336

$s= \sqrt{\frac{155.092))}{5-1}} = 6.2268$

Assuming that the data is normally distributed, also as the population sd is not given, we will use t stat

$t = \frac{\bar{x} - \mu }{s/\sqrt{n}} = \frac{11.14 - 10 }{6.2268/\sqrt{5}}= 0.409$

P value using excel formula

P value = TDIST (t statistics, df, 2) = TDIST(0.409, 4, 1)= 0.3516