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The International Air Transport Association surveys business travelers to develop quality ratings for transatlantic gateway airp

motikmotik

Answer:

The 95% confidence interval for the population mean rating is (5.73, 6.95).

Step-by-step explanation:

We start by calculating the mean and standard deviation of the sample:

$M=\dfrac{1}{n}\sum_{i=1}^n\,x_i\\\\\\M=\dfrac{1}{50}(6+4+6+. . .+6)\\\\\\M=\dfrac{317}{50}\\\\\\M=6.34\\\\\\s=\sqrt{\dfrac{1}{n-1}\sum_{i=1}^n\,(x_i-M)^2}\\\\\\s=\sqrt{\dfrac{1}{49}((6-6.34)^2+(4-6.34)^2+(6-6.34)^2+. . . +(6-6.34)^2)}\\\\\\s=\sqrt{\dfrac{229.22}{49}}\\\\\\s=\sqrt{4.68}=2.16\\\\\\$

We have to calculate a 95% confidence interval for the mean.

The population standard deviation is not known, so we have to estimate it from the sample standard deviation and use a t-students distribution to calculate the critical value.

The sample mean is M=6.34.

The sample size is N=50.

When σ is not known, s divided by the square root of N is used as an estimate of σM:

$s_M=\dfrac{s}{\sqrt{N}}=\dfrac{2.16}{\sqrt{50}}=\dfrac{2.16}{7.071}=0.305$

The degrees of freedom for this sample size are:

$df=n-1=50-1=49$

The t-value for a 95% confidence interval and 49 degrees of freedom is t=2.01.

The margin of error (MOE) can be calculated as:

$MOE=t\cdot s_M=2.01 \cdot 0.305=0.61$

Then, the lower and upper bounds of the confidence interval are:

$LL=M-t \cdot s_M = 6.34-0.61=5.73\\\\UL=M+t \cdot s_M = 6.34+0.61=6.95$

The 95% confidence interval for the mean is (5.73, 6.95).

4 0

4 years ago

70 POINTS! ∆ABC is reflected across the x-axis, then rotated 90° clockwise about the origin, and finally reflected across the li

madam [21]

Answer:

A'(1, 1); B'(3, 2); C'(1, 2)

Step-by-step explanation:

The original points are A(1,1 ), B(2, 3) and C(2, 1).

Reflecting the triangle across the x-axis will negate every y-coordinate; this maps

(1, 1)→(1, -1); (2, 3)→(2, -3); (2, 1)→(2, -1)

Rotating the figure 90° clockwise about the origin switches the x- and y-coordinates and negates the x-coordinate; this maps

(1, -1)→(-1 -1); (2, -3)→(-3, -2); (2, -1)→(-1, -2)

Reflecting across the line y=x will negate both the x- and y-coordinates; this maps

(-1, -1)→(1, 1); (-3, -2)→(3, 2); (-1, -2)→(1, 2)

3 0

3 years ago

Read 2 more answers

(30 points)PLEASE HELP! LOVE Y'ALL SO MUCH THX! If x=3b and y= 2/6b+4 , what is y in terms of x?

Anastaziya [24]

Answer:

y=(1/9)x+4

Step-by-step explanation:

x=3b

b=(1/3)x

y=2/6(1/3)x+4

y=(2/18)x+4

y=(1/9)x+4

8 0

3 years ago

Read 2 more answers

Alan, david and shari are running for president of their high school. There were a total of 1,000 votes cast for president. Davi

vekshin1

Answer:

Alan received 350 votes

Step-by-step explanation:

David received 250 votes

Shari received 400 votes

1,000 - 250=750

750 - 400 = 350

7 0

4 years ago

A researcher is interested in determining if the more than two thirds of students would support making the Tuesday before Thanks

Yakvenalex [24]

Answer:

The null hypothesis is, {H₀}: p = 0.66, H₀: p = 0.66 .

The alternative hypothesis is, {Hₐ}: p > 0.66, Hₐ: p > 0.66

Step-by-step explanation:

Let p represent the proportion of students who are supportive of making the day before Thanksgiving a holiday.

Since two populations are considered, the alternative hypothesis for the difference of the means of the two populations has to be stated.

The proportion of two-third students are supportive of making the day before Thanksgiving a holiday is p = 0.66 obtained as shown below:

The null hypothesis is,

{H₀}:p = 0.66, H₀: p = 0.66

The alternative hypothesis is,

{Hₐ:p > 0.66, Ha: p > 0.66

The null hypothesis is, {H₀}: p = 0.66, H₀: p=0.66 .

The alternative hypothesis is, {Hₐ}: p > 0.66, Hₐ: p > 0.66

3 0

3 years ago