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3 years ago

Why did we sample in statistics? Discuss with example.

1 answer:

mihalych1998 [28]3 years ago

8 0

We sample because we want to get an overview of the population. It's usually impractical to study the entire population.

For example, say you want to know what percent of people who go to a certain grocery store have a dog. It wouldn't make sense to sample every single person who goes to that grocery store; there's just too many people. But if you took a sample of say, 100 people, and asked them if they had a dog, you could get a rough estimate of all the people.

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A sample of 16 cookies is taken to test the claim that each cookie contains at least 9 chocolate chips. The average number of ch

alexandr1967 [171]

Answer:

(a) The value of z test statistics is -2.25.

(b) At 0.05 significance level the z table gives critical value of -1.645 for left-tailed test.

(c) The p-value for this test statistic is 0.0122.

(d) We conclude that the average number of chocolate chips in all the cookies is less than 9.

Step-by-step explanation:

We are given that a sample of 16 cookies is taken to test the claim that each cookie contains at least 9 chocolate chips.

The average number of chocolate chips per cookie in the sample was 7.875. The standard deviation of the population is 2.

Let $\mu$ = the average number of chocolate chips in all the cookies.

So, Null Hypothesis, $H_0$ : $\mu \geq$ 9 {means that the average number of chocolate chips in all the cookies is at least 9}

Alternate Hypothesis, $H_A$ : $\mu$ < 9 {means that the average number of chocolate chips in all the cookies is less than 9}

The test statistics that would be used here One-sample z test statistics as we know about the population standard deviation;

T.S. = $\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n} } }$ ~ N(0,1)

where, $\bar X$ = sample mean number of chocolate chips per cookie = 7.875

$\sigma$ = population standard deviation = 2

n = sample of cookies taken = 16

So, the test statistics = $\frac{7.875-9}{\frac{2}{\sqrt{16} } }$

= -2.25

(a) The value of z test statistics is -2.25.

(b) Now, at 0.05 significance level the z table gives critical value of -1.645 for left-tailed test.

Since our test statistic is less than the critical value of z as -2.25 < -1.645, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

(c) The P-value of the test statistics is given by;

P-value = P(Z < -2.25) = 1 - P(Z $\leq$ 2.25)

= 1 - 0.9878 = 0.0122

(d) Therefore, we conclude that the average number of chocolate chips in all the cookies is less than 9.

8 0

3 years ago

If 3 tacos at taco el primo cost $5.31, how much would 8 tacos cost?

Sergeu [11.5K]

Answer:

$\$14.16$

Step-by-step explanation:

Since the question implies a constant rate, we can set up the following proportion:

$\frac{3}{5.31}=\frac{8}{x},\\3x=8\cdot 5.31,\\x=\frac{8\cdot 5.31}{3}=\boxed{\$14.16}$

4 0

3 years ago

Read 2 more answers

Product is 20 the sum is -12

d1i1m1o1n [39]

Let one number be x
Let another number be y
ATQ
x + y = -12 => y = -x -12 {mark as the first equation}
xy = 20 { mark as the second equation}

Substituting value of y in second equation
x( -x - 12) = 20
-x² - 12x = 20
-x² - 12x - 20 = 0 { middle term splitting}
-x² -10x - 2x -20 = 0
-x( x + 10 ) -2 ( x +10 )
( -x - 2 ) ( x + 10 ) are the factors.
-x -2 = 0 x + 10 = 0
-x = 2 x = -10
x = -2
so we get two values of x i.e. -2 and -10
now substituting value of x in first equation ( x = -2 )
y = -x - 12 y = -x - 12
y = - ( -2 ) - 12 y = -(-10) - 12
y = 2 - 12 y = 10 - 12
y = -10 y = -2

So we get to know that if x = -2 then y = -10 And when x = -10 then y = -10.
Hope this help :)

3 0

3 years ago

To help solve the trigonometric inequality 2sin(x)=>-1, which two equations can be graphed?

soldier1979 [14.2K]

Answer:

B. y=sin(x) and y=-1/2

Step-by-step explanation:

We have been given the following trigonometric inequality;

2sin(x)=>-1

The above inequality can be re-written as;

sin(x)=>-1/2

after dividing both sides by 2.

We can then formulate two separate equations, one containing the expression on the right hand side and the other containing the expression on the left hand side;

From the left hand side we form the following equation;

y = sin(x)

From the right hand side we form the following equation;

y = -1/2

Therefore, the above two equations can be graphed to help solve the given trigonometric inequality

6 0

4 years ago

22 divided by 2,739 with the quotient and remainder

Margaret [11]

Answer:

124.5

Step-by-step explanation:

3 0

4 years ago

Read 2 more answers

Why did we sample in statistics? Discuss with example.​

Why did we sample in statistics? Discuss with example.