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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 7 pounds within a month'. A sample of 10 clients of this program are weighed on the first day of the diet and then one month later.
Client Day1 One Month Later
1 185 179
2 163 217
3 167 212
4 205 130
5 182 181
6 165 158
7 212 202
8 130 124
9 217 211
10 181 172
1. What is the p-value of the test (round to 4 decimal places)?

Respuesta :

Answer:

P-value = 0.3334

Step-by-step explanation:

We have a hypothesis test, with this null and alternative hypothesis:

[tex]H_0: \mu\geq7\\\\H_a:\mu<7[/tex]

(The null hypothesis states that the weight loss is equal or higher than 7)

The significance level is assumed as 0.05.

From the table, we have a sample mean of 2.1 and a sample standard deviation of 34.7.

The t-statistic is

[tex]t=\frac{M-\mu}{\sigma/\sqrt{n}} =\frac{2.1-7}{34.7/\sqrt{10}} =\frac{-4.9}{11}= -0.445[/tex]

For 9 degrees of freedom, the P-value for t=-0.445 is P(t<-0.445)=0.3334.

This P-value is bigger than the significance level, so the effect is not significant. The null hypothesis is not rejected.

gbenewaeternity

Answer:

The p-value is 0.4264

Step-by-step explanation:

In calculating the P-value of the test, the standard deviation and mean   differences of the weight on first day of diet and weight one month later is computed.

Arranging the data on a table, we have;

s/no  Weight on First     Weight on   M = F-L     M²       (M-Mbar)²

          Day of Diet (F)     Month (L)                

1              185                     179              6             36              15.21  

2             163                     217            -54         2916           3147.21

3             167                     212            -45         2025          2218.41

4             205                    130            75          5625          5314.41

5             182                     181              1              1                1.21

6             165                     158            7             49              24.01

7             212                     202           10           100             62.41

8             130                     124            6             36              15.21

9             217                     211             6             36              15.21

10           181                      172             9              81               47.61

TOTAL:                                             21            10735      10860.9

Mean ( M bar) =  Σ M/n    where n = 10

                       =   21/10

                       =   2.1

Standard deviation (sd) = √Σ( M - M bar)²/n-1

                                = √10860.9/10-1

                                = √10860.9/9

                                = √1206.767

                               =  34.74

Calculating the t-test value, we use the formula;

T-test = Mbar/(sd/√n)

         = 2.1/(34.74/√10

         = 2.1/ (34.74/3.16)

         = 2.1 /10.994

         = 0.1910

From t-test table, the p-value for 9 degree of freedom (n-1) is given as 0.4264

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