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.
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.
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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.
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.
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Answer:
3-1 2-4 1-3 4-2
Step-by-step explanation:
The solution consists of all of the true intervals is −4 < x < −1 x > 1.
−4<x<−1 or x>1
Inequality Form: −4<x<−1 or x>1
Interval Notation: (−4,−1) ∪ (1,∞)
x^3 + 4x^2 > x + 4
Subtract x from both sides of the inequality.
x^3 + 4x^2 − x > 4
Convert the inequality to an equation.
x^3 + 4x^2 − x = 4
Move 4 to the left side of the equation by subtracting it from both sides.
x^3 + 4x^2>x+4
2 − x − 4 = 0
Factor the left side of the equation
(x + 4)(x + 1)(x − 1) = 0
If any individual factor on the left side of the equation is equal to, the entire expression will be equal to 0
x + 4 = 0
x + 1 = 0
x − 1 = 0
Set x + 4 equal to 0 and solve for x
x = −4
Set x + 1 equal to 0 and solve for x
Inequality is the difference in social status, wealth, or opportunity between people or groups. People are concerned about social inequality.
x = −1
Set x + -1 equal to 0 and solve for x
x = 1
The final solution is all the values that make (x + 4)(x + 1)(x − 1) = 0 true
x = −4, −1, 1
Use each root to create test intervals.
x < −4
−4 < x < −1
−1 < x < 1
x > 1
Choose a test value from each interval and plug this value into the original inequality to determine which intervals satisfy the
inequality.
x < −4 ←False
−4 < x < −1 ←True
−1 < x < 1 ←False
x > 1 ←True
The solution consists of all of the true intervals.
−4 < x < −1 x > 1
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Measurement of Angle LOK = 82 degrees.
Solve for x.
Answer:
x = 14
Step-by-step explanation:
<LOJ = 3x
<KOJ = (2x + 12)°
<LOK = 82°
m<LOJ + m<KOJ = m<LOK (angle addition postulate)
3x + 2x + 12 = 82 (substitution)
5x + 12 = 82
5x = 82 - 12 (Subtraction property of equality)
5x = 70
x = 70/5 (division property of equality)
x = 14
This is due by 2:20
Answer:
The answer is 60 degrees.
Step-by-step explanation:
The three angles in any triangle add up to 180 degrees.
You know by the box at the bottom right that it's a right triangle and therefore that angle is 90 degrees. They also give you the 30 degree angle at the bottom left. So:
90 degrees + 30 degrees = 120 degrees.
180 degrees (total) - 120 degrees (first 2 angles) = 60 degrees (missing angle)
Hope this helps!
А.
current value
B.
present value
С. .
future value
Answer:
b. present money
Step-by-step explanation:
the concept that States an amount of money today is worth more than that sum amount in the future. future money is not worth much then the amount received today.