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: μD = 5; HA: μD ≠ 5
H0: μD ≥ 5; HA: μD < 5
H0: μD ≤ 5; HA: μD > 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.)
|
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: μD ≤ 5; HA: μD > 5
b)
TS =
0.394381949 =0.3944 |
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