Is urgent If a line passes through the points (2, 7) and (7,9), its slope is

Suppose that a recent article stated that the mean time spent in jail by a first-time convicted burglar is 2.5 years. A study wa

4vir4ik [10]

Using the z-distribution, it is found that since the test statistic is greater than the critical value, it can be concluded that the mean length of jail time has increased.

At the null hypothesis, it is tested if the mean length of jail time is still of 2.5 years, that is:

$H_0: \mu = 2.5$

At the alternative hypothesis, it is tested if it has increased, that is:

$H_1: \mu > 2.5$

We have the standard deviation for the population, thus, the z-distribution is used. The test statistic is given by:

$z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}$

The parameters are:

$\overline{x}$ is the sample mean.
$\mu$ is the value tested at the null hypothesis.
$\sigma$ is the standard deviation of the sample.
n is the sample size.

For this problem, the values of the parameters are: $\overline{x} = 3, \mu = 2.5, \sigma = 1.5, n = 26$

Hence, the value of the test statistic is:

$z = \frac{\overline{x} - \mu}{\frac{\sigma}{\sqrt{n}}}$

$z = \frac{3 - 2.5}{\frac{1.5}{\sqrt{26}}}$

$z = 1.7$

The critical value for a right-tailed test, as we are testing if the mean is greater than a value, with a significance level of 0.05, is of $z^{\ast} = 1.645$

Since the test statistic is greater than the critical value, it can be concluded that the mean length of jail time has increased.

A similar problem is given at brainly.com/question/24166849

5 0

2 years ago

Translate the following sentence into an equation. Then solve the equation.

AfilCa [17]

the answer is

3x+7=25

-7 -7

3x=18

3x/3=18/3

x=6

8 0

2 years ago

Read 2 more answers

Determine whether the random variable is discrete or continuous. a. The number of statistics students now reading a book. b. The

andrey2020 [161]

Answer:

Continuous random variables: c and e

Discrete random variables: a, b, d

Step-by-step explanation:

We have to identify whether the random variable is discrete or continuous.

A discrete variable is a variable whose value is obtained by counting.
A continuous random variable X takes all values in a given interval of numbers.
Thus, a continuous variable can have values in decimals but a discrete random variable cannot take values in decimals.

a. The number of statistics students now reading a book.

Discrete random variable since number of students cannot take decimal values.

b. The number of textbook authors now sitting at a computer.

Discrete random variable since number of textbooks cannot be expressed in decimals but counted.

c. The exact time it takes to evaluate 27 plus 72.

It is a continuous random variable as it may take all values within an interval of time.

d. The number of free dash throw attempts before the first shot is made.

It is a discrete random variable since the number of throws can always be whole number.

e. The time it takes to fly from City Upper A to City Upper B.

Time is a continuous random variable.

6 0

3 years ago

A spinner is separated into 4 equal pieces, as shown below:

kakasveta [241]

Getting black is 1/4 of the percentage, and spinning it 10 times gives us 10/40, because there are 40 possible colors to land on when u spin it 10 times. The last spin, is just like any other time you spin it. just because it's the last spin, doesn't make the black sector greater. So the answer is 1/4 or 25%.

8 0

3 years ago

If a ball is thrown into the air with a velocity of 42 ft/s, its height (in feet) after t seconds is given by y = 42t − 16t2. Fi

Andru [333]

$\bf y=42t-16t^2\implies \left. \cfrac{dy}{dt}=42-32t \right|_{t=1}\implies 42-32\implies 10$

8 0

3 years ago