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zheka24 [161]
2 years ago
8

A past study claims that adults in America spend an average of 17 hours a week on leisure activities. A researcher wanted to tes

t this claim. She took a sample of 10 adults and asked them about the time they spent per week on leisure activities. Their responses (in hours) are as follows:13242137152518224032Assume that the times spent on leisure activities by all adults are normally distributed. At the 5% significance level, can you conclude that the claim of this earlier study is true
Mathematics
1 answer:
8090 [49]2 years ago
5 0

Answer:

The claim is false.

Step-by-step explanation:

Given the data :

13 24 21 37 15 25 18 22 40 32

The sample mean and standard deviation can ben calculated for the given sample.

Using calculator :

Sample mean, xbar = 24.7

Sample standard deviation, s = 9.04

Sample size, n = 10

The hypothesis :

H0 : μ = 17

H1 : μ ≠ 17

The test statistic :

(xbar - μ) ÷ (s/√(n))

(24.7 - 17) ÷ (9.04/√(10))

7.7 / 2.8586990

Test statistic = 2.694

We can obtain the Pvalue, at α = 0.05 ; df = n-1 = 9

Pvalue = 0.0246

Since Pvalue < α ; we reject the null ; Hence, there is significant evidence to conclude that an adult American does not spend average of 17 hours in leisure

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Claire's mother is 4 years more than twice claire's age the sum of their ages is 58 claire's age is 16,18, or 40 years and her m
Andreyy89

Answer: Claire is 18 and her mother is 40

Step-by-step explanation:

3 0
3 years ago
What is the equation of a line that is perpendicular to −x+2y=4 and passes through the point (−2, 1) ? Enter your equation in th
ANTONII [103]
Perpendicular lines have slopes that multiply to get -1
y=mx+b is the slope intercept equation
m=slope

so get into y=mx+b form
-x+2y=4
solve for y
add x both sides
2y=x+4
divide by 2 both sides
y=(1/2)x+2
the slope is 1/2

perppendicular line slope multiplies to -1
1/2 times what=-1
times 2/1 both sides
what=-2/1=-2

y=-2x+b
find b
we are given a point is (-2,1)
when x=-2, y=1
1=-2(-2)+b
1=4+b
minus 3 both sides
-3=b

so the equation is
y=-2x-3

your teacher might want it in standard form (ax+by=c) so
add 2x both sides
2x+y=-3 is an equation


so y=-2x-3 is correct (slope intercept form)
2x+y=-3 is also correct (standard form)
6 0
3 years ago
When Carson runs the 400 meter dash, his finishing times are normally distributed with a mean of 63 seconds and a standard devia
Gnom [1K]

Answer: in 95% of races, his finishing time will be between 62 and 64 seconds.

Step-by-step explanation:

The empirical rule states that for a normal distribution, nearly all of the data will fall within three standard deviations of the mean . The empirical rule is further illustrated below

68% of data falls within the first standard deviation from the mean.

95% fall within two standard deviations.

99.7% fall within three standard deviations.

From the information given, the mean is 63 seconds and the standard deviation is 5 seconds.

2 standard deviations = 2 × 0.5 = 1

63 - 1 = 62 seconds

63 + 1 = 64 seconds

Therefore, in 95% of races, his finishing time will be between 62 and 64 seconds.

6 0
3 years ago
50 POINTSS!!!!- The figure below shows the ideal pattern of movement of a herd of cattle, with the arrows showing the movement o
olga_2 [115]

Answer:

the first option

Step-by-step explanation:

solution:

distance: d=1/4 lc (because is a quarter of a circle)

length of the circumference: lc=2 pi r

pi: constant=3.14

radius of the circle: r=80 feet

replacing pi and r in the formula of lc:

lc=2 pi r

lc=2 (3.14) (80 feet)

lc=502.4 feet

replacing lc in the formula of d:

d=1/4 lc

d=1/4 (502.4 feet)

d=502.4/4 feet

d=125.6 feet

5 0
3 years ago
Read 2 more answers
Need help with this!!
wariber [46]

Answer:

below

Step-by-step explanation:

1) slope = rise / run

2 coordinates are (-4, 0), (0, 2).

2 - 0 = 2

0 -- 4 = 4

2 / 4 = 1/2 so the slope is 0.5 or ½

2) it crosses the y axis at the average of the origin and 4.

4 + 0 = 4 / 2 = 2 so y intercept is 2.

3) in y= mx + b form

f(x) = ½x + 2, or, f(x) = 0.5x + 2

3 0
1 year ago
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