Abc company has made a claim that, on average, their diet soda has less than one calorie. a consumer testing service examined nine cans, and the amount of calories recorded were 0.90, 0.95, 1.00, 1.05, 0.85, 1.00, 0.95, 0.95 and 0.90. assume the underlying population is approximately normal. a. what are the sample mean and sample standard deviation, respectively?

b. let μ denote the true mean calories of all diet sodas produced by abc company. what hypothesis should be tested in order to show if abc’s claim is valid?

c. the appropriate statistic to test this hypothesis is

d. the value of the test statistic is

e. the appropriate number of degrees of freedom for this test statistic is

f. what conclusion can be made with 95% confidence?

a. Sample mean is 0.95  and Sample standard deviation is ≈0.058

b. : μ=1 calorie  and : μ<1 calori

c. The appropriate statistic to test this hypothesis is t-statistic.

d. The value of the test statistic is -2,586

e. The appropriate number of degrees of freedom for this test statistic is 8

f. In 95% confidence, the claim that, on average, their diet soda has less than one calorie is true.

Step-by-step explanation:

a.

Sample mean is 0.95 (0.90+ 0.95+1.00+ 1.05+ 0.85+1.00+ 0.95+0.95+0.90)÷9

Sample standard deviation is ≈0.058 (sum of square differences from the mean)

b.

μ denote the true mean calories of all diet sodas produced by ABC Company.

Then

: μ=1 calorie

: μ<1 calori

c.

The appropriate statistic to test this hypothesis is t-statistic.

d.

The value of the test statistic is

t= where

t= ≈ -2,586

e.

The appropriate number of degrees of freedom for this test statistic is 8

f.

in 95% confidence, the result is significant, since one tail t(critical) with 8 degrees of freedom is bigger than t(sample) i.e. -1.860 > -2,586

We reject the null hypothesis in favor of the alternative hypothesis. Therefore the claim that, on average, their diet soda has less than one calorie is true.

answer: option a.

step-by-step explanation:

you know that the quadrilateral opqr ( a four sided figure) is inscribed in circle. this means that all its vertices are on the circle.

then, by definition, the opposite angles of the quadrilateral are supplementary, this means that the sum of their measures is 180 degrees.

you can observe in the figure that the angles ∠opq   and the angle ∠orq   are opposite, therefore:

then, can be used to d to calculate the measure of ∠opq