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PilotLPTM [1.2K]

4 years ago

15

When courtney collected her change she realized she had five times as many dimes as quarters. her dimes and quarters totaled $5.

25. how many quarters did she have?

1 answer:

Juli2301 [7.4K]4 years ago

4 0

Dimes (0.10): 5Q

Quarters (0.25): Q

Dimes + Quarters = Total

0.10(5Q) + 0.25(Q) = 5.25

0.50Q + 0.25Q = 5.25

0.75Q = 5.25

$\frac{0.75Q}{0.75}$ = $\frac{5.25}{0.75}$

Q = 7

Answer: 7 quarters

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Answer:

The test statistic is t = 2.5.

The p-value of the test is of 0.007 < 0.05, which means that the evidence supports the manufacturer's claim at the .05 significance level.

Step-by-step explanation:

Mean life of 600 hours. Test if it is more.

At the null hypothesis, we test if the mean is of 600 hours, that is:

$H_0: \mu = 600$

At the alternative hypothesis, we test if the mean is of more than 600 hours, that is:

$H_1: \mu > 600$

The test statistic is:

$t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}$

In which X is the sample mean, $\mu$ is the value tested at the null hypothesis, s is the standard deviation and n is the size of the sample.

600 is tested at the null hypothesis:

This means that $\mu = 600$

Suppose 100 bulbs were tested and found to have a mean of 625 hours with a standard deviation of 100.

This means that $n = 100, X = 625, s = 100$ .

Value of the test-statistic:

$t = \frac{X - \mu}{\frac{s}{\sqrt{n}}}$

$t = \frac{625 - 600}{\frac{100}{\sqrt{100}}}$

$t = 2.5$

The test statistic is t = 2.5.

P-value of the test and decision:

The p-value of the test is the probability of finding a sample mean above 625 hours, which is a right-tailed test, with t = 2.5 and 100 - 1 = 99 degrees of freedom.

Using a t-distribution calculator, this p-value is of 0.007.

The p-value of the test is of 0.007 < 0.05, which means that the evidence supports the manufacturer's claim at the .05 significance level.

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(2,5) (7,9) (3,9) (5,8)

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Answer:

Step-by-step explanation:

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