QUESTION Diego measured the length of a pen to be 22 cm. The actual length of the pen is 23 cm.

A certain pen has been designed so that true average writing lifetime under controlled conditions (involving the use of a writin

Morgarella [4.7K]

Answer:

(a) We reject our null hypothesis.

(b) We fail to reject our null hypothesis.

(c) We fail to reject our null hypothesis.

Step-by-step explanation:

We are given that a certain pen has been designed so that true average writing lifetime under controlled conditions (involving the use of a writing machine) is at least 10 hr.

A random sample of 18 pens is selected.

Let $\mu$ = true average writing lifetime under controlled conditions

So, Null Hypothesis, $H_0$ : $\mu \geq$ 10 hr {means that the true average writing lifetime under controlled conditions is at least 10 hr}

Alternate Hypothesis, $H_A$ : $\mu$ < 10 hr {means that the true average writing lifetime under controlled conditions is less than 10 hr}

The test statistics that is used here is one-sample t test statistics;

T.S. = $\frac{\bar X -\mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample mean

s = sample standard deviation

n = sample size of pens = 18

n - 1 = degree of freedom = 18 -1 = 17

Now, the decision rule based on the critical value of t is given by;

If the value of test statistics is more than the critical value of t at 17 degree of freedom for left-tailed test, then we will not reject our null hypothesis as it will not fall in the rejection region.

If the value of test statistics is less than the critical value of t at 17 degree of freedom for left-tailed test, then we will reject our null hypothesis as it will fall in the rejection region.

(a) Here, test statistics, t = -2.4 and level of significance is 0.05.

Now, at 0.05 significance level, the t table gives critical value of -1.74 at 17 degree of freedom.

Here, clearly the value of test statistics is less than the critical value of t as -2.4 < -1.74, so we reject our null hypothesis.

(b) Here, test statistics, t = -1.83 and level of significance is 0.01.

Now, at 0.051 significance level, the t table gives critical value of -2.567 at 17 degree of freedom.

Here, clearly the value of test statistics is more than the critical value of t as -2.567 < -1.83, so we fail to reject our null hypothesis.

(c) Here, test statistics, t = 0.57 and level of significance is not given so we assume it to be 0.05.

Now, at 0.05 significance level, the t table gives critical value of -1.74 at 17 degree of freedom.

Here, clearly the value of test statistics is more than the critical value of t as -1.74 < 0.57, so we fail to reject our null hypothesis.

8 0

3 years ago

Find the volume of the triangular prism.

krok68 [10]

Approximately 673.76

4 0

3 years ago

A piece of wood is 12 feet long and a nail is 3 inches long. The piece of wood is how many times as long as the nail?

Softa [21]

The piece of wood is 48 times as long as the nail (12 feet = 144 inches) because 3 goes into 144 48 times.

7 0

3 years ago

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A softball has a diameter of 3.82 inches. How many square inches of material is necessary to cover a softball? Use 3.14 for π

lisabon 2012 [21]

Answer:

45.82 square inches

Step-by-step explanation:

Use the formula for the surface area of a sphere, A = 4 $\pi$ r²

If the diameter is 3.82 inches, the radius is 1.91 inches.

Plug in 3.14 as $\pi$ and 1.91 as r, and solve:

A = 4 $\pi$ r²

A = 4(3.14)(1.91²)

A = 45.82

So, approximately 45.82 square inches of material are needed.

6 0

3 years ago

The graph of part of linear function p is shown on the grid.

Rufina [12.5K]

Answer:

A

Step-by-step explanation:

The domain of a function is the span of x-values covered by the graph.

From the graph, we can see that it stretches from x=-7 to x=2.

However, note that at x=-7, the dot is closed (shaded in). In other words, x=-7 is in our domain.

On the other hand, at x=2, the dot is not shaded. So, x=2 is not included in our domain.

Therefore, our domain all are numbers between -7 and 2 including -7 (and not including 2).

As a compound inequality, this is:

$-7\leq x$

So, our answer is A.

Also note that we use x instead of p(x) because the domain relates to the x-variable. If we were to instead find the range, then we would use p(x).

4 0

3 years ago

Read 2 more answers