Answer:
11.474
Explanation:
a. To calculate the range, we subtract the smallest value from the largest value:
Range = largest value - smallest value
Range = 40 - 12
Range = 28
Therefore, the range is 28.
b. To calculate the MAD (Mean Absolute Deviation), we first need to find the mean of the data set:
Mean = (38 + 40 + 15 + 12 + 24) / 5
Mean = 25.8
Next, we find the absolute deviation of each value from the mean:
|38 - 25.8| = 12.2
|40 - 25.8| = 14.2
|15 - 25.8| = 10.8
|12 - 25.8| = 13.8
|24 - 25.8| = 1.8
Then, we find the average of these absolute deviations:
MAD = (12.2 + 14.2 + 10.8 + 13.8 + 1.8) / 5
MAD = 10.56 (rounded to 2 decimal places)
Therefore, the MAD is 10.56.
c. To calculate the population variance, we first need to find the mean of the data set (which we already calculated in part b):
Mean = 25.8
Next, we calculate the sum of the squared differences between each value and the mean:
(38 - 25.8)^2 = 147.24
(40 - 25.8)^2 = 206.01
(15 - 25.8)^2 = 110.88
(12 - 25.8)^2 = 189.54
(24 - 25.8)^2 = 2.56
Then, we find the average of these squared differences:
Population Variance = (147.24 + 206.01 + 110.88 + 189.54 + 2.56) / 5
Population Variance = 131.646 (rounded to 2 decimal places)
Therefore, the population variance is 131.646.
d. To calculate the population standard deviation, we take the square root of the population variance:
Population Standard Deviation = sqrt(131.646)
Population Standard Deviation = 11.474 (rounded to 2 decimal places)
Therefore, the population standard deviation is 11.474.
Calculate the geometric mean return for the following data set:
-5% 6% -7% 4.7% 5.1%
(Negative Value should be indicated by minus sign. Round your intermediate calculations to at least 4 decimal places and final answer to 2 decimal places.)
The geometric mean return for the given data set is approximately 0.85%.
To calculate the geometric mean return for the given data set, we need to follow these steps:
Convert the percentage returns into decimal form.
To do this, we divide each return by 100:
-5% becomes -0.05
6% becomes 0.06
-7% becomes -0.07
4.7% becomes 0.047
5.1% becomes 0.051
Add 1 to each decimal return to obtain the growth factor:
-0.05 + 1 = 0.95
0.06 + 1 = 1.06
-0.07 + 1 = 0.93
0.047 + 1 = 1.047
0.051 + 1 = 1.051
Multiply all the growth factors together:
0.95 × 1.06 × 0.93 × 1.047 × 1.051
= 1.04251741
Take the nth root of the product, where n is the number of returns in the data set. In this case, n = 5:
[tex]1.04251741^{(1/5)}[/tex] ≈ 1.008488
Subtract 1 from the result and multiply by 100 to obtain the geometric mean return as a percentage:
(1.008488 - 1) × 100 ≈ 0.8488
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The population standard deviation for the heights of dogs, in inches, in a city is 3.7 inches. If we want to be 95% confident that the sample mean is within 2 inches of the true population mean, what is the minimum sample size that can be taken?
z0.10 z0.05 z0.025 z0.01 z0.005
1.282 1.645 1.960 2.326 2.576
Use the table above for the z-score, and be sure to round up to the nearest integer.
The minimum sample size needed to estimate the population mean with a specified margin of error can be calculated using the formula: n = (z * σ / E)^2, where z is the z-score, σ is the population standard deviation, and E is the margin of error. For a 95% confidence level and a margin of error of 2 inches, with a population standard deviation of 3.7 inches, the minimum sample size is approximately 2885.
To calculate the minimum sample size needed to estimate the population mean with a specified margin of error, we can use the formula:
n = (z * σ / E)^2
Where:
n = sample size
z = z-score corresponding to the desired confidence level
σ = population standard deviation
E = margin of error
In this case, the population standard deviation (σ) for the heights of dogs is given as 3.7 inches. We want to be 95% confident that the sample mean is within 2 inches of the true population mean.
The corresponding z-score for a 95% confidence level can be obtained from the provided table, which is 1.960.
Substituting the given values into the formula, we have:
n = (1.960 * 3.7 / 2)^2
Calculating this expression, we find:
n ≈ (7.252 * 7.4)^2
n ≈ 53.6776^2
n ≈ 2884.82
Rounding up to the nearest integer, the minimum sample size that can be taken is 2885.
Therefore, the correct answer is z0.025 = 1.960.
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Apparent magazine reports that the average amount of wireless data used by teenagers each month is seven gigs bites for her science fair project Ellis that’s out to prove the magazine is wrong she claims that the Mina Monchhichi teenagers in her area is less than a report Ella collects information from a simple random sample for teenagers at her high school and calculate the mean of 5.8 GB per month with a standard deviation of 1.9 Gigamon bytes per month assume the population distribution is approximately normal test Ella’s claim at 0.005 level of significance State to null and alternative paths hypothesis for this test for this test
Ella's hypothesis is that the average wireless data usage of teenagers in her area is less than seven gigabytes per month, and she aims to test this using a one-sample t-test with a significance level of 0.005.
How to State a Null and Alternative Hypotheses?Null hypothesis (H0): The average amount of wireless data used by teenagers in Ella's area is not less than seven gigabytes per month.
Alternative hypothesis (Ha): The average amount of wireless data used by teenagers in Ella's area is less than seven gigabytes per month.
Ella aims to test if the mean data usage in her sample provides evidence to reject the claim made by the magazine. She collects data from a simple random sample at her high school, where the sample mean is 5.8 GB per month and the standard deviation is 1.9 GB per month.
Assuming the population distribution is approximately normal, Ella will conduct a one-sample t-test at a 0.005 level of significance to determine if there is sufficient evidence to support her claim.
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Justin a manager with the ITA team was suggested a few changes in the GTB by one of his clients. Whose approval should justin take on the modified terms
A store is having a sale on chocolate chips and walnuts, for 2 pounds of chocolate chips and 5 pounds of walnuts , the cost ia $17. For 8 pounds of chocolate chips and three pounds of walnuts, the total cost for each pound of chocolate chips and each pound of walnuts
If a store is having a sale on chocolate chips and walnuts, for 2 pounds of chocolate chips and 5 pounds of walnuts. The total cost for 8 pounds of chocolate chips and 3 pounds of walnuts is $68 for the chocolate chips and $10.20 for the walnuts.
What is the total cost?Let's calculate the cost per pound for each item:
Cost per pound of chocolate chips = Total cost / Total pounds of chocolate chips
Cost per pound of chocolate chips = $17 / 2 pounds
Cost per pound of walnuts = $17 / 5 pounds
Cost per pound of walnuts = Total cost / Total pounds of walnuts
Cost per pound of chocolate chips = $8.50/pound
Cost per pound of walnuts = $3.40/pound
For 8 pounds of chocolate chips and 3 pounds of walnuts
Total cost for 8 pounds of chocolate chips = Cost per pound of chocolate chips * Total pounds of chocolate chips
Total cost for 8 pounds of chocolate chips = $8.50/pound * 8 pounds = $68
Total cost for 3 pounds of walnuts = Cost per pound of walnuts * Total pounds of walnuts
Total cost for 3 pounds of walnuts = $3.40/pound * 3 pounds = $10.20
Therefore the total cost for 8 pounds of chocolate chips and 3 pounds of walnuts is $68 for the chocolate chips and $10.20 for the walnuts.
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How d you solve a match paired test
Answer:
Try looking it up on Khan Academy.
Explanation:
They have very good explanations.