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3 years ago

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In a hypothesis test, the claim is μ≤25 while the sample of 34 has a mean of 21 and a population standard deviation of 5.9 from

a normally distributed data set. In this hypothesis test, would a z test statistic be used or a t test statistic and why?

1 answer:

iogann1982 [59]3 years ago

5 0

Answer:

z test statistic

Step-by-step explanation:

Given : In a hypothesis test, the claim is μ ≤ 25 while the sample of 34 has a mean of 21 and a population standard deviation of 5.9 from a normally distributed data set.

To Find : In this hypothesis test, would a z test statistic be used or a t test statistic and why?

Solution:

Claim : μ ≤ 25

Sample size = n = 34

Population Standard Deviation = 5.9

Since n > 30 and we are given the standard deviation of population .

So, we will use z test statistics .

Hence In this hypothesis test, z test statistic would be used.

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Jason and Alison are hiking in the woods when they spot a rare owl in a tree. Jason stops and measures an angle of elevation of

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Answer:

$Owl= 67.14ft$

Step-by-step explanation:

<em>See comment for complete question.</em>

The given information is represented in the attached figure.

First convert 22°8'6'' and 30° 40’ 30” to degrees

$22^{\circ} 8'6'' = 22 + \frac{8}{60} + \frac{6}{3600}$

$22^{\circ} 8'6'' = 22.135^{\circ}$

$30^{\circ} 40'30'' = 30 + \frac{40}{60} + \frac{30}{3600}$

$30^{\circ} 40'30'' = 30.675^{\circ}$

Considering Jason's position:

$tan(22.135^{\circ}) = \frac{H}{x + 48}$

Where x = distance between the tree and Alison

Make H the subject

$H = (x + 48)tan(22.135^{\circ})$

Considering Alison's position

$tan(30.675^{\circ}) = \frac{H}{x}$

Make H the subject

$H = xtan(30.675^{\circ})$

$H = H$

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$(x + 48) *0.4068 = x* 0.5932$

Open bracket

$x *0.4068 + 48 *0.4068 = 0.5932x$

$0.4068x + 19.5264 = 0.5932x$

Collect Like Terms

$-0.5932x+0.4068x = -19.5264$

$-0.1864x = -19.5264$

$0.1864x = 19.5264$

Make x the subject

$x = \frac{19.5264}{0.1864}$

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Substitute 104.76 for x in $H = xtan(30.675^{\circ})$

$H = 104.76 * tan(30.675^{\circ})$

$H = 104.76 * 0.5932$

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A body travels 10 meters during the first 5 seconds of its travel, and it travels a total of 30 meters over the first 10 seconds

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v = d/t

We need to calculate the speed of the second 5 seconds of the travel:
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