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3 years ago

There is a line of of best fit using the points (165,168) and (174,178) what is the equation ?

Mathematics

1 answer:

Xelga [282]3 years ago

8 0

Answer:

y = 10/9x - 46/4 OR y = 10/9x -15.3

Step-by-step explanation:

1. Find the slope of the points (change in y over the change in x)

(174, 178)

(165, 168)

10/9

2. Plug into y = mx + b to find the y-intercept of the equation (I am using point 165, 168)

168 = 10/9(165) + b

3. Solve

168 = 10/9(165) + b

168 = 550/3 + b

-46/3 = b OR -15.3 = b

3. Plug in the slope and the y-intercept into y = mx + b

y = 10/9x - 46/4 OR y = 10/9x -15.3

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Answer:

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Statistics In the manual “How to Have a Number One the Easy Way,” it is stated that a song “must be no longer than three minutes

dimaraw [331]

Answer:

We conclude that the sample is from a population of songs with a mean greater than 210 seconds.

Step-by-step explanation:

We are given that a simple random sample of 40 current hit songs results in a mean length of 252.5 seconds.

Assume that the standard deviation of song lengths is 54.5 sec.

Let $\mu$ = population mean length of the songs

So, Null Hypothesis, $H_0$ : $\mu$ $\leq$ 210 seconds {means that the sample is from a population of songs with a mean smaller than or equal to 210 seconds}

Alternate Hypothesis, $H_A$ : $\mu$ > 210 seconds {means that the sample is from a population of songs with a mean greater than 210 seconds}

The test statistics that will be used here is One-sample z-test statistics because we know about population standard deviation;

T.S. = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\bar X$ = sample mean length of songs = 252.5 seconds

$\sigma$ = population standard deviation = 54.5 seconds

n = sample of current hit songs = 40

So, the test statistics = $\frac{252.5-210}{\frac{54.5}{\sqrt{40} } }$

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The value of z-test statistics is 4.932.

Now, at 0.05 level of significance, the z table gives a critical value of 1.645 for the right-tailed test.

Since the value of our test statistics is more than the critical value of z as 4.932 > 1.645, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.

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