Amanda's gross annual salary is $62,112 what is the maximum amount of rent she can afford to pay

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

2 years ago

Pleaseeeeeeeeeeeeeeeeee hellpppppppp urgent. pleaseeeeeeee

Nastasia [14]

Answer:

first u have to write in the equation

Step-by-step explanation:

ooops my ph is hanged

3 0

3 years ago

What is 8/32 in simplest form

Lyrx [107]

So the question is what is 8/32 in the simplest form. To find out we need to simplify the fraction. In this case the nominator and the denominator are both multiple of 8 so the nominator is 8=1*8 and 32=4*8 so we can write (1*8)/(4*8) and we see that we can cancel out number 8 and get 1/4 which is the simplest form of the fraction.

5 0

2 years ago

Read 2 more answers

Please Help

leonid [27]

The answer is D because microcosm is a community displaying characteristics of something larger.

4 0

3 years ago

You randomly choose a marble from a jar. The jar contains 3 red marbles, 10

GrogVix [38]

Total marbles=3+10+8+4=25 marbles total
10 blue marbles/25 total marbles
10/25=2/5 probability

7 0

3 years ago