What single angle is the vertical angle to

Answers

Answer 1

Answer:

The supplement of <DCE is <ACE, remember, a supplementary pair is a pair of two angles whose sum of degrees sums up to 180 degrees.

The verticle angle to <BCD is <ACF. A verticle angle is formed when two lines intersect, there are four angles formed, the verticle angles are the angles opposite to each other, and verticle angles are congruent.

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This is true statement.

Sample space is made from all the possible outcomes that an event can have.
For example when tossing a coin, the possible outcomes are Head and Tail so the sample space will be {Head, Tail}.

Thus, option A is the correct answer

To evaluate the effect of a treatment, a sample of n=8 is obtained from a population with a mean of μ=40 , and the treatment is administered to the individuals in the sample. After treatment, the sample mean is found to be M=35 .

a. If the sample variance is s^2=32 , are the data sufficient to conclude that the treatment has a significant effect using a two-tailed test with alpha=.05

b. If the sample variance is s^2=72 , are the data sufficient to conclude that the treatment has a significant effect using a two-tailed test with alpha=.05 ?

c. Comparing your answer for parts a and b, how does the variability of the scores in the sample influence the outcome of a hypothesis test?

Answers

Final answer:

A hypothesis test was conducted to evaluate the treatment's effect. For both variances, we failed to reject the null hypothesis, so we can't conclude that the treatment had a significant effect. The variability of scores plays a crucial role, as more variability makes it harder to identify a significant effect.

Explanation:

To determine if the treatment has a significant effect, we perform a hypothesis test using the sample mean (M), sample variance (s^2), and population mean (μ). The null hypothesis is that there's no effect from the treatment (μ=M), while the alternative hypothesis is that there is an effect (μ≠M).

a. For sample variance s^2=32, we can use the formula for the t score: t = (M - μ)/(s/√n) = (35 - 40)/(√32/√8) = -2.24. Based on a two-tailed t-distribution table, the critical t values for α=.05 and 7 degrees of freedom (n-1) are approximately -2.365 and 2.365. Our t value (-2.24) lies within this range, so we fail to reject the null hypothesis. We cannot conclude that the treatment has a significant effect.

b. Repeat the same process with sample variance s^2=72. The t value is now (35 - 40)/(√72/√8) = -1.48, again falling within the range of the critical t values. We can't conclude that the treatment has a significant effect.

c. As the variability (s^2) of the sample scores increases, it becomes more difficult to find a significant effect. Higher variability introduces more uncertainty, which can mask actual changes caused by the treatment.

Learn more about Hypothesis Testing here:

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Final answer:

To evaluate the effect of a treatment using a two-tailed test with alpha = 0.05, we compare the calculated t-value to the critical t-value. The sample variance influences the outcome of the hypothesis test, with a larger variance leading to a wider critical region.

Explanation:

a. To test if the treatment has a significant effect, we will conduct a two-tailed hypothesis test using the t-distribution. The null hypothesis states that the treatment has no effect (μ = 40), while the alternative hypothesis states that the treatment has an effect (μ ≠ 40). With a sample size of 8, degrees of freedom (df) will be n-1 = 7. We will use the t-test formula to calculate the t-value, and compare it to the critical t-value from the t-table with α = 0.05/2 = 0.025. If the calculated t-value falls outside the critical region, we reject the null hypothesis and conclude that the treatment has a significant effect.

b. Similar to part a, we will conduct a two-tailed t-test using the same null and alternative hypotheses. With a sample size of 8, df = n-1 = 7. We will calculate the t-value using the sample mean, population mean, and sample variance. Comparing the calculated t-value to the critical t-value with α = 0.05/2 = 0.025, if the calculated t-value falls outside the critical region, we reject the null hypothesis and conclude that the treatment has a significant effect.

c. The variability of the scores in the sample, as indicated by the sample variance, influences the outcome of the hypothesis test. In both parts a and b, the sample variance is given. A larger sample variance (s^2 = 72 in part b) indicates more variability in the data, meaning the scores in the sample are more spread out. This leads to a larger t-value and a wider critical region. Therefore, it becomes easier to reject the null hypothesis and conclude that the treatment has a significant effect.