Mathematics, 15.07.2021 19:10 shavonfriend27

A psychologist suspects that heroin addicts have a different assessment of self-worth than others in the general population. On a test designed to measure self-worth, the mean for the general population is 48.6. The psychologist obtains a random sample of 40 test scores produced by heroin addicts and found the sample mean and the sample standard deviations are 45.5 and 8.5, respectively. Do these data indicate the self-worth of heroin addicts is less than that of the general population?

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The p-value of the test if 0.0131, which is less than the standard significance level of 0.05, meaning that these data indicates that the self-worth of heroin addicts is less than that of the general population.

Step-by-step explanation:

On a test designed to measure self-worth, the mean for the general population is 48.6.

At the null hypothesis, we test if the mean is of 48.6, that is:

$H_0: \mu = 48.6$

A psychologist suspects that heroin addicts have a different assessment of self-worth than others in the general population. Test if it is lower.

At the alternative hypothesis, we test if the mean is lower, that is:

$H_1: \mu < 48.6$

The test statistic is:

We have the standard deviation for the sample, which means that the t-distribution is used to solve this question.

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

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.

48.6 is tested at the null hypothesis:

This means that $\mu = 48.6$

The psychologist obtains a random sample of 40 test scores produced by heroin addicts and found the sample mean and the sample standard deviations are 45.5 and 8.5, respectively.

This means that n = 40, X = 45.5, s = 8.5

Value of the test statistic:

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

$t = \frac{45.5 - 48.6}{\frac{8.5}{\sqrt{40}}}$

t = -2.31

P-value of the test:

The p-value of the test is a one-tailed test(mean lower than a value), with t = -2.31 and 40 - 1 = 39 df.

Using a t-distribution calculator, this p-value is of 0.0131.

Answer from: Quest

45.36 feet per second

step-by-step explanation:

tyrone travels 30 miles in 58.2 minutes.

1 mile = 5280 feet; this means he travels

30(5280) = 158400 feet in 58.2 minutes.

1 minute = 60 seconds; this means he travels 158400 feet in

58.2(60) = 3492 seconds.

this gives us the unit rate of

158400/3492 = 45.36 feet per second.

Answer from: Quest

when the daily mileage is greater than 40 miles, unlimited mileage plan will save you money. 40 miles is the break-even point.

step-by-step explanation:

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