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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

3 years ago

Please help, thank you!!

julsineya [31]

Answer:

Step-by-step explanation:

Givens

Triangle
Base = 11 inches
Height = 12 inches

Formula

A = Base * height / 2

Solution

Area = 11 * 12/2
Area = 132 /2
Area = 66 square inches.

4 0

2 years ago

Read 2 more answers

Identify az of this sequence: 0.25, 0.5, 0.75, 1, 1.25. 1.5

4vir4ik [10]

<h3><u>Question:</u></h3>

Identify a3 of this sequence: 0.25, 0.5, 0.75, 1, 1.25, 1.5,...a3=

<h3><u>Answer:</u></h3>

The third term of sequence is 0.75

$a_3 = 0.75$

<h3><u>Solution:</u></h3>

Given that, sequence is:

0.25, 0.5, 0.75, 1, 1.25. 1.5

Let us find the difference between terms

$0.5 - 0.25 = 0.25\\\\0.75-0.5 = 0.25\\\\1.25-1=0.25\\\\1.5-1.25=0.25$

This is a arithmetic sequence

Because the difference between any term and its immediately preceding term is always 0.25

In a arithmetic sequence,

$a_1 = \text{ first term of sequnece }\\\\a_2 = \text{second term of sequnce }\\\\a_3 = \text{third term of sequnece }\\\\a_n = \text{ nth term of sequnce }$

Thus, in the sequence 0.25, 0.5, 0.75, 1, 1.25. 1.5

$a_3 = \text{ third term } = 0.75$

Thus the third term of sequence is 0.75

5 0

3 years ago

There are 8 members on a board of directors. if they must form a subcommittee of 6 members, how many different subcommittees are

Shtirlitz [24]

1. Given a group of n people. There are C(n, r) ways of forming groups of r out of n.

2. Where C(n, r)= $\frac{n!}{r!(n-r)!}$

3. For example, given {Andy, John, Julia}. We want to pick 2 people to give a gift: we can pick {(Andy, John), (Andy, Julia), (John, Julia)}, so there are 3 ways. So we can list and count.

4. Or we could do this with the formula C(3, 2)= $\frac{3!}{2!(1)!}= \frac{3*2*1}{2*1}=3$

5. C(8, 6)= $\frac{8!}{2!6!}= \frac{8*7*6!}{2*6!}= \frac{8*7}{2}= 4*7=28$

So there are C(8,6)=28 ways of chosing 6 out of 8 people to form the subcommittees. <span />

5 0

3 years ago

Which description does NOT guarantee that a quadrilateral is a square?

faltersainse [42]

A would be the correct answer

8 0

2 years ago

Help me please Thanks