Mathematics, 18.03.2021 01:10 xxaurorabluexx

During the first 13 weeks of the television season, the Saturday evening 8:00 P. M. to 9:00 P. M. audience proportions were recorded as ABC 29%, CBS 28%, NBC 25%, and independents 18%. A sample of 300 homes two weeks after a Saturday night schedule revision yielded the following viewing audience data: ABC 95 homes, CBS 65 homes, NBC 87 homes, and independents 53 homes. Test with = .05 to determine whether the viewing audience proportions changed. Required:
Compute the value of the 2 test statistic (to 2 decimals). The p value is Has a significant change occurred in viewing audience proportions?

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Answer from: juansoto227711

- The value of the 2 test statistic is 6.98

- There is no sufficient evidence to reject the claim of the specific distribution

Step-by-step explanation:

Given

Proportion (p)

$ABC = 29\% = 0.29\\CBS = 28\% = 0.28\\NBC = 25\% = 0.25\\Others = 18\% = 0.18\\$

Samples

$ABC = 95\\CBD = 65\\NBC = 87\\Others = 53\\\alpha = 0.05$

First, we formulate a table for chi square totals:

$x^2 = \frac{(O - E)^2}{E}$

Where

O = Observed Frequency and E = Expected Frequency

So, we have:

$\begin{array}{cccccc}{\ } & {O} & {E = np} & {O - E} & {(O -E)^2} & {x^2 = \frac{(O - E)^2}{E}} \ \\ \\ {0.29} & {95} & {87} & {8} & {64} & {0.736} &{0.28} & {65} & {84} & {-19} & {361} & {4.300} & {0.25} & {87} & {75} & {12} & {144} & {1.920} & {0.18} & {53} & {54} & {-1} & {1} & {0.019}\ \end{array}$

For ABC

E = np = 300 * 0.29= 87

O-E =95 - 87 = 8

(O-E)^2 = 8^2 = 64

$x^2 = \frac{(O - E)^2}{E} = \frac{64}{87} = 0.736$

For CBS

E =np = 300 * 0.28 = 84

O -E = 65 - 84 = -19

(O -E)^2 = (-19)^2 = 361

$x^2 = \frac{(O - E)^2}{E} = \frac{361}{84} = 4.300$

For NBC

E =np = 300 * 0.25 = 75

O -E = 87 - 75 = 12

(O -E)^2 = (12)^2 = 144

$x^2 = \frac{(O - E)^2}{E} = \frac{144}{75} = 1.920$

For others:

E = np = 300 * 0.18 =54

O - E = 53 - 54 = -1

(O - E)^2 = (-1)^2= 1

$x^2 = \frac{(O - E)^2}{E} = \frac{1}{54} = 0.019$

$\sum x^2 = 0.736 + 4.300 + 1.920 + 0.019$

$\sum x^2 = 6.975$

$\sum x^2 = 6.98$ --- approximated

The value of the 2 test statistic is 6.98

Next, is to determine the p value:

Calculate the degree of freedom

df = n - 1

df = 4 - 1

df = 3

Using the x^2 table in the 3rd row,

$\sum x^2 = 6.98$ corresponds to:

p = 0.072699

The value of p is:

0.05 < P < 0.10

This implies that, we fail to reject H o

Answer from: Quest

the range of a function is the range of y-values for which it is defined, or exists. given that we are only looking at the y-values, we can already discount the first two answers as they deal with the domain of the function (range of x-values).

now, what we need to do is find the smallest and highest y-values for which the function is defined. if you'd like, you could take a ruler and start at the very bottom of the graph, find the lowest point, then move the ruler higher and higher until you reach the highest point. doing so either in your head or with an actual ruler, we can see that the lowest y-value is -5 and the highest y-value is -1.

the question now remains as to whether they are included in the range (fourth answer) or excluded (third answer). the key here is to recognise whether they are marked with an open or a closed circle. since both (-2, -5) and (2, -1) are marked with a closed circle, they are points that exist on the graph and are thus included in the range (note that if they were marked with an open circle like (4, -2) then that would signify that there is a break in the graph at that point).

thus, the fourth answer, (y | -5 ≤ y ≤ -1), is correct.

also note that usually it is good practice to scan your eye inbetween the highest and lowest point for any breaks in the graph - we do have one here at (4, -2), however -2 is still included in the range because there is another point that is included in the graph with the same y-value, ie. point (1, -2).

i hope that but if you require any further explanation don't hesitate to comment below.

Me if you can and if you finished this lesson on edg- comment you.

Answer from: Quest

v = 1/3 a^2h

step-by-step explanation:

the volume is 1/3 a^2h.

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During the first 13 weeks of the television season, the Saturday evening 8:00 P. M. to 9:00 P. M. au...

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