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Paul [167]
3 years ago
15

What is your favorite color? A large survey of countries, including the United States, China, Russia, France, Turkey, Kenya, and

others, indicated that most people prefer the color blue. In fact, about 24% of the population claim blue as their favorite color.† Suppose a random sample of n = 52 college students were surveyed and r = 12 of them said that blue is their favorite color. Does this information imply that the color preference of all college students is different (either way) from that of the general population? Use α = 0.05. (a) What is the level of significance?
Mathematics
1 answer:
Ipatiy [6.2K]3 years ago
7 0

Answer:

Step-by-step explanation:

We would set up the hypothesis test.

For the null hypothesis,

p = 0.24

For the alternative hypothesis,

p ≠ 0.24

This is a two tailed test

Considering the population proportion, probability of success, p = 0.24

q = probability of failure = 1 - p

q = 1 - 0.24 = 0.76

Considering the sample,

Sample proportion, P = r/n

Where

r = 12

n = 52

P = 12/52 = 0.23

We would determine the test statistic which is the z score

z = (P - p)/√pq/n

z = (0.23 - 0.24)/√(0.24 × 0.76)/52 = - 0.17

Recall, population proportion, P = 0.24

The difference between sample proportion and population proportion(p - P) is 0.24 - 0.23 = 0.01

Since the curve is symmetrical and it is a two tailed test, the p for the left tail is 0.24 - 0.01 = 0.23

the p for the right tail is 0.24 + 0.01 = 0.25

These proportions are lower and higher than the null proportion. Thus, they are evidence in favour of the alternative hypothesis. We will look at the area in both tails. Since it is showing in one tail only, we would double the area

From the normal distribution table, the area below the test z score in the left tail 0.43

We would double this area to include the area in the right tail of z = 0.17 Thus

p = 0.43 × 2 = 0.86

The level of significance is 5%

Since alpha, 0.05 < than the p value, 0.86, then we would fail to reject the null hypothesis. Therefore, at 5% significance level, this information does not imply that the color preference of all college students is different (either way) from that of the general population.

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anastassius [24]

Answer:

0.291 is the closest

Step-by-step explanation:

ok so 0.8/y=2 3/4

first of all turn it into a decimal

2 3/4= 2.75

2.75=0.8/y

0.8/?=2.75

3 0
3 years ago
How is the precision used in measuring the length and width of a rectangle related to the precision of the resulting area measur
steposvetlana [31]
The more precise your length and width are, the more precise your area <span>measurement will be. Take this as example:

</span>width = 9.3045 mm
<span>length = 8.023 mm
</span><span>
Let's first round up:

width = 9.3 mm
length = 8 mm
Area = 9.3*8 = 74.4 mm

But if you are more precise with the width and length:

</span>width = 9.3045 mm
<span>length = 8.023 mm
</span>Area = 9.3045 *  8.023 = <span>74.6500035 mm

The more precise your length and width are, the more precise your area is. Also, as you can see t</span>he more precise your length and width are, the more your area will increase and will be more accurate.<span>
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3 0
3 years ago
The side length, s, of a cube is 4x^2+3. If V=s^3, what is the volume of the cube?
sweet [91]

The volume of the cube is (4x^{2} +3)(4x^{2} +3)(4x^{2} +3).


To simplify this, use the FOIL method between the first two terms, and then the product and the last term:

(4x^{2} +3)(4x^{2} +3)(4x^{2} +3)\\(16x^{4}+12x^{2}  +12x^{2} +9)(4x^{2} +3)\\(16x^{4}+24x^{2} +9)(4x^{2} +3)\\(64x^{6}+48x^{4} +96x^{4}+72x^{2}  +36x^{2}+27)\\ 64x^{6}+144x^{4}+108x^{2} +27


The answer is the first choice.


Hope this helps!!

7 0
3 years ago
The length of each side of the square is represented by x-2 and the perimeter is 48 inches
shtirl [24]
48 = 4(x-2)

48 = 4x -8
56= 4x

14=x
x-2 = 12
one side is 12 inches long
8 0
3 years ago
A particular fruit's weights are normally distributed, with a mean of 406 grams and a standard deviation of 27 grams.The heavies
Tom [10]

Given

mean of 406 grams and a standard deviation of 27 grams.

Find

The heaviest 14% of fruits weigh more than how many grams?

Explanation

given

mean = 406 gms

standard deviation = 27 gms

using standard normal table ,

\begin{gathered} P(Z>z)=14\% \\ 1-P(Zso , [tex]\begin{gathered} x=z\times\sigma+\mu \\ x=1.08\times27+406 \\ x=435.16 \end{gathered}

Final Answer

Therefore , The heaviest 14% of fruits weigh more than 435.16 gms

8 0
1 year ago
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