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AURORKA [14]
3 years ago
6

250 students were asked to choose their favorite color. How many more students chose purple than red as their favorite color? 26

% chose purple and 22% chose red
Mathematics
1 answer:
nevsk [136]3 years ago
6 0

Answer:

10 more students chose purple than red as their favorite color

Step-by-step explanation:

Step 1

Determine the proportion of students that chose each color

purple=26%

red=22%

Step 2

Use the expression for the number of students per color as follows;

Number of students per color=proportion per color×total number of students

for purple;

proportion that chose purple=26%

total number of students=250

replacing;

Number of students that chose purple=(26/100)×250=65 students

for red;

proportion that chose red=22%

total number of students=250

replacing;

Number of students that chose purple=(22/100)×250=55 students

Step 3

Difference=65-55=10

10 more students chose purple than red as their favorite color

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denpristay [2]

Answer:

We conclude that the population mean light bulb life is at least 500 hours at the significance level of 0.01.

Step-by-step explanation:

We are given that a manufacturer produces light bulbs that have a mean life of at least 500 hours when the production process is working properly. The population standard deviation is 50 hours and the light bulb life is normally distributed.

You select a sample of 100 light bulbs and find mean bulb life is 490 hours.

Let \mu = <u><em>population mean light bulb life.</em></u>

So, Null Hypothesis, H_0 : \mu \geq 500 hours      {means that the population mean light bulb life is at least 500 hours}

Alternate Hypothesis, H_A : \mu < 500 hours     {means that the population mean light bulb life is below 500 hours}

The test statistics that would be used here <u>One-sample z test statistics</u> as we know about the population standard deviation;

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

where, \bar X = sample mean bulb life = 490 hours

           σ = population standard deviation = 50 hours

           n = sample of light bulbs = 100

So, <u><em>the test statistics</em></u>  =  \frac{490-500}{\frac{50}{\sqrt{100} } }

                                     =  -2

The value of z test statistics is -2.

<u>Now, at 0.01 significance level the z table gives critical value of -2.33 for left-tailed test.</u>

Since our test statistic is higher than the critical value of z as -2 > -2.33, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which <u>we fail to reject our null hypothesis.</u>

Therefore, we conclude that the population mean light bulb life is at least 500 hours.

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3 years ago
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Answer:

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Step-by-step explanation:

4.16

because thousanth is 5

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Step-by-step explanation:

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