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kirill115 [55]
3 years ago
8

The average local cell phone call length was reported to be 2.27 minutes. A random sample of 20 phone calls showed an average of

2.98 minutes in length with a standard deviation of 0.98 minutes.
At α = 0.05 can it be concluded that the average differs from the population average?
Report your answer to two decimal places.
Note: Find the test statistic ONLY to test this claim using an appropriate formula. You must show your work.
Mathematics
1 answer:
Afina-wow [57]3 years ago
6 0

Answer:

Yes, at α = 0.05 it can be concluded that the average differs from the population average.

Step-by-step explanation:

We are given that the average local cell phone call length was reported to be 2.27 minutes. A random sample of 20 phone calls showed an average of 2.98 minutes in length with a standard deviation of 0.98 minutes.

<em>Let </em>\mu<em> = population average local cell phone call length</em>

SO, Null Hypothesis, H_0 : \mu = 2.27 minutes  {means that the average is same as that of population average}

Alternate Hypothesis, H_a : \mu \neq 2.27 minutes  {means that the average differs from the population average}

The test statistics that will be used here is <u>One-sample t test statistics </u>because we don't know about population standard deviation;

                T.S.  =  \frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }  ~ t_n_-_1

where, \bar X = sample average call length = 2.98 minutes

            s = sample standard deviation = 0.98 minutes

            n = sample of phone calls = 20

So, <em><u>test statistics</u></em>  =  \frac{2.98-2.27}{\frac{0.98}{\sqrt{20} } }  ~ t_1_9

                               =  <u>3.24</u>

Now, at 0.05 level of significance the t table gives critical values between -2.093 and 2.093 at 19 degree of freedom for two-tailed test. Since our test statistics does not lie within these range of critical values so we have sufficient evidence to reject our null hypothesis as test statistics will fall in the rejection region.

Therefore, we conclude that the average differs from the population average.

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tickets for a cinema costs £4 and £5. There were 223 customers who paid a total of £936. How many bought £4 tickets
noname [10]

The number of people who bought £4 tickets are 139.

<h3>How to illustrate the equation?</h3>

Let £4 tickets be x

Let £5 tickets be y.

Therefore based on the information given, this will be:

x + y = 223 ..... i

4x + 5y = 936 ..... ii

From equation i

x = 213 - y

Put this into equation ii

4x + 5y = 936

4(213 - y) + 5y = 936

852 - 4y + 5y = 936

Collect like terms

y = 84

This implies that the number of £5 tickets is 84.

Recall that x + y = 223

x + 84 = 223

x = 223 - 84

x = 139

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3 0
1 year ago
Which equation is the slope-intercept form of the line that passes through (6, –11) and is parallel to the graph of y = –23x + 1
Finger [1]

Answer:

Equation of other line passing through point (6 , - 11) and parallel to given line is  y = - 23 x + 127 .

Step-by-step explanation:

Given as :

The equation of one line

y = - 23 x + 12

∵ The equation of line in slope-intercept form is

y = m x + c

where m is the slope of line and c is y-intercept

Now, Compare given line with standard line equation

So, The slope of given line = m = - 23

Now, Again

Other line is passing through point (6 , - 11) and is parallel to given line

so, both the lines are parallel

For parallel line condition , Slope of both lines are equal

Let The slope of other line = M

So, M = m = - 23

Now, Equation of other line passing through point (6 , - 11) and slope - 23 in slope-point form

y - y_1 = M × (x -  x_1)

i.e y - ( - 11) = (- 23) × (x - 6)

Or, y + 11 = - 23 × x + 138

Or, y = - 23 x + 138- 11

i.e y = - 23 x + 127

So, The equation of other line  y = - 23 x + 127

Hence, Equation of other line passing through point (6 , - 11) and parallel to given line is  y = - 23 x + 127 . Answer

8 0
3 years ago
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gayaneshka [121]
8-5(3x-7)

Distribute:
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Combine like terms:
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So, 'D' would be your answer.
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