Question

A diet center claims that it has the most effective weight loss program in the region. Its advertisements say, “Participants in our program lose more than 5 pounds within a month.” Six clients of this program are weighed on the first day of the diet and then one month later. Let the difference be defined as Weight on First Day of Diet minus Weight One Month Later. (You may find it useful to reference the appropriate table: z table or t table)

Client	Weight on First Day of Diet	Weight One Month Later
1	155	171
2	186	190
3	174	165
4	201	182
5	163	153
6	157	130

Let the difference be defined as Before – After.

a. Specify the null and alternative hypotheses that test the diet center’s claim.

• H₀: μ_D = 5; H_A: μ_D ≠ 5

• H₀: μ_D ≥ 5; H_A: μ_D < 5

• H₀: μ_D ≤ 5; H_A: μ_D > 5

b. Assuming that weight loss is normally distributed, calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)

	Test statistic

Answer 1

t-Test: Paired Two Sample for Means
	Weight on First Day of Diet	Weight One Month Later
Mean	172.6666667	165.1666667
Variance	326.6666667	463.7666667
Observations	6	6
Pearson Correlation	0.705673455
Hypothesized Mean Difference	5
df	5
t Stat	0.394381949
P(T<=t) one-tail	0.354779435
t Critical one-tail	2.015048373
P(T<=t) two-tail	0.709558871
t Critical two-tail	2.570581836

a)

option C)

H₀: μ_D ≤ 5; H_A: μ_D > 5

b)

TS =

0.394381949 =0.3944