Question

A new​ weight-loss program claims that participants will lose an average of more than 10 pounds after completing it. The accompanying data table shows the weights of eight individuals before and after the program. Complete parts​ (a) through​ (e) below.

Person		Before	After
1		226	203
2		213	195
3		206	195
4		186	173
5		204	195
6		199	181
7		243	232
8		191	193

. a. Perform a hypothesis test using alphaαequals=0.10 to determine if the average weight loss was more than 10 pounds for participants in the​ weight-loss program. Let muμd be the population mean of​ matched-pair differences for the weight before the program minus the weight after the program. State the null and alternative hypotheses. Choose the correct answer below. A. Upper H 0H0​: mu Subscript dμdless than or equals≤10 Upper H 1H1​: mu Subscript dμdnot equals≠10 B. Upper H 0H0​: mu Subscript dμdnot equals≠10 Upper H 1H1​: mu Subscript dμdequals=10 C. Upper H 0H0​: mu Subscript dμdless than or equals≤10 Upper H 1H1​: mu Subscript dμdgreater than>10 Your answer is correct.D. Upper H 0H0​: mu Subscript dμdless than<10 Upper H 1H1​: mu Subscript dμdgreater than or equals≥10 E. Upper H 0H0​: mu Subscript dμdless than or equals≤10 Upper H 1H1​: mu Subscript dμdless than<10 F. Upper H 0H0​: mu Subscript dμdequals=10 Upper H 1H1​: mu Subscript dμdnot equals≠10

b. Calculate the appropriate test statistic and interpret the results of the hypothesis test using alpha equals 0.10 (α=0.10). The test statistic is? ​(Round to two decimal places as​ needed.)

c. identify and interpret p

d. construct a 98% confidence interval to estimate average weight loss. UCL = ? LCL =? (Interpret)

e. what assumptions need to be made in order to perform this process?

Answer 1

Answer: A new weight-loss program claims that participants will lose an average of more than 10 pounds after completing it. The accompanying data table shows the weights of eight individuals before and after the program.

Solution:

Person	before	after	difference	difference^2
1	226	203	23	529
2	213	195	18	324
3	206	195	11	121
4	186	173	13	169
5	204	195	9	81
6	199	181	18	324
7	243	232	11	121
8	191	193	-2	4
Total			101	1673

e) Assumption need to perform this process:

The samples are dependent, the distribution of matched pair difference between the measurements for the the population is approximately normal if number of match pair is less than 30.