Answer:
(i) To find the margin of error for the 95% confidence interval for the proportion of households that have cable television, we need to use the formula for the margin of error for a sample proportion. This formula is given by
ME = z * sqrt(p * (1 - p) / n)
where ME is the margin of error, z is the critical value for the desired confidence level, p is the sample proportion, and n is the sample size. In this case, p is 0.18, n is 550, and the critical value for a 95% confidence interval is 1.96. Plugging these values into the formula, we get
ME = 1.96 * sqrt(0.18 * (1 - 0.18) / 550) = 0.0215
Therefore, the margin of error for the 95% confidence interval is 2.15%.
(ii) To write the confidence interval in the interval form, we need to add and subtract the margin of error from the sample proportion. The sample proportion is 0.18, and the margin of error is 0.0215, so the confidence interval is given by
0.18 +/- 0.0215 = (0.1585, 0.2015)
Therefore, the 95% confidence interval for the proportion of households that have cable television is (0.1585, 0.2015).
Explanation:
Which of the following is not true of women’s hand?
a.
It had a refined, subtle emotional impact.
b.
It was used mainly by secular painters.
c.
It was characterized by delicate lines and asymmetrical compositions.
d.
It was a style only used by women.
Mandalas are composed of sections that are all arranged around a single central point and are composed of circles enclosed within squares. Usually, they are created on paper or cloth, with threads drawn on a surface, in metal, or with stone. Thus, option D is correct.
What is the role of women’s hand?Delicate lines, powerful muted colors, and asymmetrical compositions were characteristics of women's hands. It was designed to have a sophisticated, delicate emotional effect. Polytheistic religions had an influence on the esoteric Buddhist arts.
Therefore, gender role expectations exist in every country, ethnic group, and culture, but they can vary greatly among them.
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Answer:
d. It was a style only used by women.
Explanation:
Explanation with steps
Considering the available information, the mean of this student's quiz scores is 14.2
What is the Mean score?Mean score is a term that is used to describe the number gotten from adding all the scores together, then dividing by the number of scores you added.
Therefore, in this case, to find the mean score, we have the following;
Step 1: Add all the scores togetherStep 2: Divide the sum by the number of scores used8 + 13 + 15 + 15 + 16 + 18 = 85
85 ÷ 6 = 14.166 ≈ 14.2 (the nearest tenth of a point)
The student's median quiz score.Step 1: Take the two middle numbers of the even-numbered setStep 2: Add the two numbers togetherStep 3: Divide the total by 28, 13, 15, 15, 16, 18
The two middle number is 15 + 15 = 30
Divide the total by 2 = 15.
Hence, the median quiz score is 15.
The student's mode quiz score.Step 1: Look at all the data scoresStep 2: Identify the data score that appears most oftenThe data score that appears most often here is 15
because it appears twice.
Hence, in this case, it is concluded that the median and mode of the student's quiz score are the same, while the mean score is 14.2
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4. Which of the following statements are True?
1. The sum of all exterior angles of any polygon equals 180
II. The Exterior Angle of a triangle is equal to the sum of its remote interior
angles.
III. All Equilateral Triangles are Isosceles and therefore have essentially the
same properties as Isosceles Triangles.
IV. The sum of any two sides of a triangle is greater than or equal to the third
side.
O II, III and IV
O II, and III
O All of these choices
I, II and IV
I, II and III
Answer:
The correct answer is I, II and IV.
Statement I is true. The sum of all exterior angles of any polygon is always equal to 360 degrees.
Statement II is true. The exterior angle of a triangle is equal to the sum of the two interior angles that are not adjacent to it.
Statement III is false. An equilateral triangle is a type of triangle in which all sides are equal in length, but it is not necessarily isosceles (i.e., it does not necessarily have two equal angles).
Statement IV is true. This statement is known as the triangle inequality theorem, and it states that the sum of the lengths of any two sides of a triangle must be greater than or equal to the length of the third side.
Together, these statements imply that the correct answer is I, II and IV.
Explanation:
1. The following figures show the distribution of the digits in numbers chosen at random
from a telephone directory
Digit 0
1 2
3
4 5 6 7 8 9
Frequency 1026 1107 997 966 1075 933 1107 972 964 853
Test whether the digits may be taken to occur equally in the directory.
Total
10,000
Note that since from the results, the null hypothesis is rejected, it can be deduced that there is strong proof that the distribution of digits in the directory is NOT uniformly distributed.
What is a null hypothesis?The null hypothesis in inferential statistics states that the two options are the same. The null hypothesis states that the observed difference is solely attributable to chance. The likelihood that the null hypothesis is true may be calculated using statistical testing.
In the above scenario, the chi-square statistics will be used.
Sample size; n = 10
Chi-square test statistic is:
X²ₙ₋₁ = (Oi - Ei)² /Ei
Where Oi = Observed Frequency; and
Ei = Expected Frequency
Note that the Mathematical Expression for Expected Frequency is:
Ei = (O₁ + O₂ + .....+ Oₙ)/n
= (1026 + 1107 + ....+ 853)/10
= 10,000/10
= 1,000
The hypotheses is described as:
H₀: The distribution of digits in the directory follows a uniform distribution.
Hₐ: The distribution of digits in the directory does not follow a uniform distribution.
From the above, the test statistics using a spreadsheet are computed as follows: X²[tex]_{cal}[/tex] test statistic = 58.542
Next, we examine the Degree of Freedom (DF).
Df = (n-1)
= 10 - 1
= 9
Thus, the critical value computed using X² distribution table is 16.92.
Since X²[tex]_{cal}[/tex] (58.542) > X²[tex]_{tab}[/tex] (16.92), the null hypothesis is rejected. Hence, it is correct to state that there is good evidence that the distribution of digits in the telephone directory is no uniformly distributed.
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