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The manufacturer of an MP3 player wanted to know whether a 10% reduction in price is enough to increase the sales of its product

Effectus [21]

The pooled estimate of the variance is 187.650 and the test statistic is -2.32

<h3>Pooled estimate of the variance</h3>

The dataset is given as:

Regular price 138 124 89 112 116 123 98

Reduced price 124 134 154 135 118 126 133 132

Let the regular price be dataset 1 and the reduced price be dataset 2.

So, we have:

#1: 138 124 89 112 116 123 98

#2: 124 134 154 135 118 126 133 132

Calculate the sample means and the sample standard deviations using a graphing calculator.

$\sigma_1 = 16.56$

$\bar x_1 = 114.29$

$\sigma_1^2 = 274.24$

$\sigma_2 = 10.65$

$\bar x_2 = 132$

$\sigma_2^2 = 113.43$

The pooled estimate of the variance is:

$\sigma_p^2 = \frac{\sigma_1^2(n_1 - 1) + \sigma_2^2(n_2 - 1)}{(n_1 - 1) + (n_2 - 1)}$

This gives

$\sigma_p^2 = \frac{274.24 * (7 - 1) + 113.43 * (8 - 1)}{(7- 1) + (8- 1)}$

Evaluate the factors

$\sigma_p^2 = \frac{2439.45}{13}$

Divide

$\sigma_p^2 = 187.65$

Hence, the pooled estimate of the variance is 187.650

<h3>The test statistic</h3>

This is calculated using:

$t = \frac{\bar x_1 - \bar x_2}{\sqrt{\sigma_p^2} * \sqrt{\frac{1}{n_1} + \frac{1}{n_2}}}$

This gives

$t = \frac{114.29 - 132}{\sqrt{187.650} * \sqrt{\frac{1}{7} + \frac{1}{6}}}$

This gives

$t = \frac{-17.71}{\sqrt{187.650} * \sqrt{\frac{13}{42}}}$

Evaluate the product

$t = \frac{-17.71}{\sqrt{58.08214}}$

Evaluate the exponent

$t = \frac{-17.71}{7.62}$

Divide

t = -2.32

Hence, the test statistic is -2.32

<h3>The decision about the null hypothesis</h3>

The critical value at 0.025 significance level is -1.96

-2.32 is less than -1.96

This means that we accept the null hypothesis

Read more about test statistic at:

brainly.com/question/14128303

#SPJ1

6 0

2 years ago

Screen measures 30 cm wide n 22 cm high what is the diagonal measure of the screen

Scorpion4ik [409]

I think you'd use the pythagoran theorem for this (a squared + b squared = c squared). So 30 squared plus 22 squared equals the diagonal measure squared. This is 900 + 484 = c squared. That's 1384. The square root of that is 37.

8 0

3 years ago

Sin 60° x tan 45° what is that is for a homework

Ugo [173]

Answer:

75 degrees

Step-by-step explanation:

60 = 45= 75 = 180

Because every triangle has 180 degrees in it

6 0

2 years ago

Find the next three terms in the arithmetic sequence: -33, -24, -15, -6, ...

katen-ka-za [31]

Answer:

7, 22, 39 hope this helps :)

Step-by-step explanation:

It’s adding 7, then 9, then 11, and so on.

4 0

2 years ago

Briana has 4 1/2 cups of oats. She uses 2 1/4 cups of oats to make oatmeal- raisins cookies, then borrow 1 cup of oats from her

insens350 [35]

Answer:

She has enough with $\frac{3}{4}$ cups left over.

Step-by-step explanation:

For this equation, it's probably easiest to use improper fractions.

At the start, she has 4 $\frac{1}{2}$ cups, or $\frac{9}{2}$ , which can be converted to $\frac{18}{4}$ (which is useful for the next part) by multiplying the numerator and denominator by 2.

When she uses 2 $\frac{1}{4}$ cups, which can be converted to $\frac{9}{4}$ . When subtracting this from the original, you get $\frac{18}{4}$ - $\frac{9}{4}$ = $\frac{9}{4}$ .

She borrows another cup, or $\frac{4}{4}$ of a cup, which gets added on to the previous result, giving $\frac{9}{4}$ + $\frac{4}{4}$ = $\frac{13}{4}$ .

The recipe calls for 2 $\frac{1}{2}$ cups, which can be converted to $\frac{5}{2}$ or $\frac{10}{4}$ .

$\frac{13}{4}$ - $\frac{10}{4}$ = $\frac{3}{4}$ , meaning she has $\frac{3}{4}$ cups left over.

** solving this mainly uses conversion to improper fractions and adding/subtracting fractions, which may be skills you would like to practice. I'm always happy to help!

6 0

2 years ago