A spinner has 5 equally sized sections, 1 of which is gray and 4 of which are blue. The spinner is spun twice. What is the proba
1 answer:
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Answer:
k = 4 units
Step-by-step explanation:
Using Pythagoras' identity on the right triangle.
The square on the hypotenuse is equal to the sum of the squares on the other 2 sides, that is
k² + 7.5² = 8.5²
k² + 56.25 = 72.25 ( subtract 56.25 from both sides )
k² = 16 ( take the square root of both sides )
k = = 4
Answer:
Step-by-step explanation:
<u>Confidence Interval</u>
When the population standard deviation is known, the formula for a confidence interval for a population mean
is:
Where n is the sample size and z is the corresponding z-value from the standard normal distribution for the selected confidence level. The value of z for a 95% confidence interval is z=1.96. The rest of the values are
Calculating the confidence interval
Or, equivalently
Answer:
Step-by-step explanation:
Hello!
The objective of the study is to determine whether the magnets are effective in treating pain. For these two independent groups of individuals with equal affections were randomly sampled, one was treated with magnets and the other group of individuals, call it control group, was treated with a placebo treatment.
The information for both samples is:
X₁: pain measurement using a visual analog scale after the individual received magnet treatments.
X₁~N(μ₁;σ₁²)
n₁= 20
X[bar]₁= 0.46
S₁= 0.93
X₂: pain measurement using a visual analog scale of an individual of the control groups.
X₂~N(μ₂;σ₂²)
n₂= 20
X[bar]₂= 0.41
S₂= 1.26
The claim is that the pain reductions of the control group have more variation than the pain reductions of the target group. If it's so then we could suspect that the population variance of the control group, σ₂², will be greater than the population variance of the magnet group, σ₁².
To test the relationship between these two population variances you have to conduct a variance ratio test using the Snedecors F statistic.
The hypotheses are:
H₀: σ₂² ≤ σ₁²
H₁: σ₂² > σ₁²
α: 0.05
This hypothesis test is one-tailed to the right, there is only one critical value:
The decision rule for the test is:
If ≥ 2.17, then the decision is to reject the null hypothesis.
If < 2.17, then the decision is to not reject the null hypothesis.
Since the calculated value of F is less than the critical value, the decision is to reject the null hypothesis. So using a 5% significance level the decision is to not reject the null hypothesis, you can conclude that the population variance of the pain reduction of the control group is less or equal than the population variance of the pain reduction on individuals treated with magnets.
I hope it helps!