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The following table shows the weights of nine subjects before and after following a particular diet for two months. Test the cla

Annette [7]

Using the t-distribution, it is found that there is not enough evidence that the diet is helping people lose weight.

<h3>What are the hypothesis tested?</h3>

At the null hypothesis, it is tested if the mean hasn't decreased, that is:

$H_0: \mu_B \leq \mu_A$

$H_0: \mu_B - \mu_A \leq 0[qtex]At the alternative hypothesis, it is tested if the mean has decreased, that is:[tex]H_1: \mu_B - \mu_A > 0[qtex]What are the mean and the standard error for the distribution of differences?For each sample, they are given as follows:[tex]\mu_B = 170.44, s_B = \frac{29.275}{\sqrt{9}} = 9.7583$ .

$\mu_A = 160.56, s_A = \frac{24.203}{\sqrt{9}} = 8.067$ .

Hence, for the distribution of differences, they are:

$\overline{x} = \mu_B - \mu_A = 170.44 - 160.56 = 9.88$ .

$s = \sqrt{s_B^2 + s_A^2} = \sqrt{9.7583^2 + 8.067^2} = 11.66$

<h3>What is the test statistic and the decision?</h3>

The test statistic is:

$t = \frac{\overline{x} - \mu}{s}$

In which $\mu = 0$ is the value tested at the null hypothesis.

Hence:

$t = \frac{\overline{x} - \mu}{s}$

$t = \frac{9.88 - 0}{11.66}$

t = 0.85.

Considering a right-tailed test with 9 + 9 - 2 = 16 df, with a standard significance level of 0.05, the critical value is t = 1.7459. Since t = 0.85 < 0.85, there is not enough evidence that the diet is helping people lose weight.

More can be learned about the t-distribution at brainly.com/question/13873630

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2 years ago

Each row in the table below shows one possible set of angle measurements for this drawing

creativ13 [48]

Applying the definitions of angles on a straight line and vertical angles, the missing angle measurementts are given in the table atached below.

<h3>What are Angles on a Straight Line?</h3>

Angles found on a straight line equals 180 degrees.

<h3>What area Vertcial Angles?</h3>

Vertical angles are congruent angles that lie directly opposite each other.

Second Row:

m∠LGK = 45° (given in the diagram)

m∠IGH = 35° (given in the table)

m∠KGJ = m∠IGH (vertical angles)

m∠KGJ = 35°

m∠JGI = 180 - m∠KGJ (angles on a straight line)

m∠JGI = 180 - 35 = 145°

m∠HGL = 180 - m∠LGK - m∠IGH (angles on a straight line)

m∠HGL = 180 - 45 - 35 = 100°

Third Row:

m∠LGK = 45° (given in the diagram)

m∠HGL = 97° (given in the table)

m∠KGJ = 180 - m∠HGL - m∠LGK (angles on a straight line)

m∠KGL= 180 - 97 - 45 = 38°

m∠JGI = 180 - m∠KGJ (angles on a straight line)

m∠JGI = 180 - 38 = 142°

m∠IGH = m∠KGL (vertical angles)

m∠IGH = 38°

Thus, applying the definitions of angles on a straight line and vertical angles, the missing angle measurementts are given in the table atached below.

Learn more about straight line and vertical angles on:

brainly.com/question/14362353