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2 years ago

11

On a can of sardines it is written that the can contains 10 sardines. You open up 100 cans and find the average is 9.75 sardines

with a standard deviation of 1.
What is the test statistic in a test of the null hypothesis that the population average is 10?

1 answer:

kkurt [141]2 years ago

5 0

Answer: $t= -2.5$

Step-by-step explanation:

By considering the given statements :

Null hypothesis : $\mu=10$

Alternative hypothesis : $\mu\neq10$ ( opposite of null hypothesis.)

As per given , we have

Sample size : n= 100

Sample mean : $\overline{x}=9.75$

Sample standard deviations : $s=1$

Since population standard deviation is unknown , so we will perform t-test.

Formula for test statistic ( for population mean):

$t=\dfrac{\overline{x}-\mu}{\dfrac{s}{\sqrt{n}}}\\\\=\dfrac{9.75-10}{\dfrac{1}{\sqrt{100}}}\\\\=\dfrac{-0.25}{\dfrac{1}{10}}=-0.25\times10=-2.5$

Hence, the required test statistic : $t= -2.5$

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In a standard television set, the screen height is 0.75 times the screen width. If a television set measures 34 inches along the

S_A_V [24]

We can solve this by using the P<span>ythagorean theorem which is below:

$a^2 + b^2 = c^2$

Or we can say
</span> $w^2 + h^2 = d^2$
<span>w = widht
h = height
d = diagonal measure

With that said, we know the height is .75 times the width so .75w. We also know d = 34, which is our diagonal measure.
w = don't know yet but need to find
h = .75w
d = 34
Now lets plugin the information we know into our equation

</span> $w^2 + h^2 = d^2$
$w^2 + (.75w)^2 = 34^2$
Now lets to the math
$w^2 + (.75w)^2 = 34^2$
$w^2 + (.75w)^2 = 1156$
$w^2 + .5625w^2 = 1156$
Combine like terms
$w^2 + .5625w^2 = 1156$
$1.5625w^2 = 1156$
Divide both sides of the equal sign by 1.5625
$\frac{1.5625w^2}{1.5625} = \frac{1156}{1.5625}$
$w^2 = 739.84$
Now take the square root on both sides of the equal sign
$\sqrt{w^2} = \sqrt{739.84}$
$w = 27.2$

So the width is 27.2
We can check this by putting 27.2 back into our original equation
$w^2 + (.75w)^2 = 34^2$
$27.2^2 + (.75\times 27.2)^2 = 34^2$

3 0

2 years ago

Find amplitude and midline of the function y=4cos(4)-5.

Nat2105 [25]

Amplitude: 4

If midline means center, it is -5
I'm also implying that there is an x in cos(4x)

7 0

3 years ago

wolverine [178]

Answer: c the third option

Step-by-step explanation:

4 0

2 years ago

Read 2 more answers

You roll two fair dice, one green and one red. (a) Are the outcomes on the dice independent? Yes No (b) Find P(1 on green die an

ASHA 777 [7]

Answer:

a

Yes

b

$P(1 \& 5) = \frac{1}{36}$

c

$P(5 \& 1) = \frac{1}{36}$

d

$P(5 \& 1 | 1\& 5 ) = \frac{1}{18}$

Step-by-step explanation:

From the question we are told that

Two fair dice, one green and one red were rolled

Generally the outcomes on the dice independent because the outcome on the first dice is not affected by the second die

Generally the probability of getting a 1 on a dice rolled is $P(1) = \frac{1}{6}$

the probability of getting a 5 on a dice rolled is $P(5) = \frac{1}{6}$

Generally the probability of P(1 on green die and 5 on red die) is mathematically represented as

$P(1 \& 5) = \frac{1}{6} *\frac{1}{6}$

$P(1 \& 5) = \frac{1}{36}$

Generally the probability of P(5 on green die and 1 on red die) is mathematically represented as

$P(5 \& 1) = \frac{1}{6} *\frac{1}{6}$

$P(5 \& 1) = \frac{1}{36}$

Generally the probability of P((1 on green die and 5 on red die) or (5 on green die and 1 on red die)) is mathematically represented as

$P(5 \& 1 | 1\& 5 ) = \frac{1}{36} + \frac{1}{36}$

$P(5 \& 1 | 1\& 5 ) = \frac{1}{18}$

8 0

2 years ago

In the June 2007 issue, Consumer Reports also examined the relative merits of top-loading and front-loading washing machines, te

saveliy_v [14]

Answer:

Yes

Step-by-step explanation:

Given that in the June 2007 issue, Consumer Reports also examined the relative merits of top-loading and front-loading washing machines, testing samples of several different brands of each type.

The difference in mean values test gave a p value of 0.32

Confidence level = 95%

Alpha = 1-0.95 = 0.05

Compare p with alpha, here p >alpha

Hence we accept null hypothesis that there is no difference in the means.

Confidence interval method also will yield the same result. i.e. confidence interval for difference of means would definitely contain 0 at 95% conf level.

So answer is yes

3 0

2 years ago