Mathematics : asked on mia12340
 15.10.2022

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Mathematics
Step-by-step answer
P Answered by Specialist

400 NUMBERS. I WENT THROUGH AND TOOK OUT ALL THE 5's AND 6's AND THEN I PUT IT THROUGH A WORD COUNTER AND GOT 400

Step-by-step explanation:

3 2  2  2 4 2 3

2 2  3  1  4

2 2  3 2  4  3 3

1 1 2 1 3  3 3 2 3

3 3 3  2 1 3 1

4  2  4 4  1

1 1 1  1 2 1 4 2

3 2 4 3 4  3 2 2 3

4 1  3 2 3  3 3

3 2 4 2 3 4 3  1 4

4 3 1  3 2 3 2  4

2 4 3  1  2 3

3 3 1  1 3 4 2

1 3  3 4 2  4 4 4

1  1 3 3 4 1 2 4

4 4 4

2 3 4  3 1  1

2 2 4  4 1 1 1 2 3

3  3 2

3 3 3 2 3 1 1

3 4 1 3  3

3 4 2  2 4 1

3  4  4

4  2 4 3 2 4

1  4 4 1 2  1

4 3 4  1 2  4

3  4 1  1 2 3 1 1

3 1 3 3 1  4 4 3 1

1 3 4 4 1 1  3 1

4 4 1  1  1

2 1 1  1 4 2 1

2  1 4  4 1  4 3

2 1  3 1 3 4 2 2 2

4 4 1  2 3  2

3  1 1  1  1

4  4 3  4

4  4  1 1 1  2

1  1 1 3 2 2  1

4 1  2  2  2 2

3 1 2  2 1 3 4 2

1 3 1 1 4  4 1 1 2

1 3 4 3 4 2 2 3 3

1  4 1 3 1 1 4 2

4 4 4 1 1  4

3  1 4  2  1

2  1 1 2  3  3

1 3  2  1  3

1 4 1 2  1 1 3

2 4 4 2 1  2 2 2

4 2 2  4 1 3  2

1 4 1 1

4  4  1 1  4  2

2 2 2 2 3  1 3 3

4  1 4 4 1 4  1

3  2 1 1 3 1 2 4 4

4 1  4  1 5 3

3  2 2  2  4

1 4  3 4 3  2

3 3 2 4 2  2

4 1  3 4 3 1 2 4


How many numbers are lower than 5

3 2 5 2 6 6 2 4 2 3
2 2 6 6 3 6 6 1 6 4
2 2 6 3 2 6 4 5 3 3
1 1 2
Mathematics
Step-by-step answer
P Answered by Master

400 NUMBERS. I WENT THROUGH AND TOOK OUT ALL THE 5's AND 6's AND THEN I PUT IT THROUGH A WORD COUNTER AND GOT 400

Step-by-step explanation:

3 2  2  2 4 2 3

2 2  3  1  4

2 2  3 2  4  3 3

1 1 2 1 3  3 3 2 3

3 3 3  2 1 3 1

4  2  4 4  1

1 1 1  1 2 1 4 2

3 2 4 3 4  3 2 2 3

4 1  3 2 3  3 3

3 2 4 2 3 4 3  1 4

4 3 1  3 2 3 2  4

2 4 3  1  2 3

3 3 1  1 3 4 2

1 3  3 4 2  4 4 4

1  1 3 3 4 1 2 4

4 4 4

2 3 4  3 1  1

2 2 4  4 1 1 1 2 3

3  3 2

3 3 3 2 3 1 1

3 4 1 3  3

3 4 2  2 4 1

3  4  4

4  2 4 3 2 4

1  4 4 1 2  1

4 3 4  1 2  4

3  4 1  1 2 3 1 1

3 1 3 3 1  4 4 3 1

1 3 4 4 1 1  3 1

4 4 1  1  1

2 1 1  1 4 2 1

2  1 4  4 1  4 3

2 1  3 1 3 4 2 2 2

4 4 1  2 3  2

3  1 1  1  1

4  4 3  4

4  4  1 1 1  2

1  1 1 3 2 2  1

4 1  2  2  2 2

3 1 2  2 1 3 4 2

1 3 1 1 4  4 1 1 2

1 3 4 3 4 2 2 3 3

1  4 1 3 1 1 4 2

4 4 4 1 1  4

3  1 4  2  1

2  1 1 2  3  3

1 3  2  1  3

1 4 1 2  1 1 3

2 4 4 2 1  2 2 2

4 2 2  4 1 3  2

1 4 1 1

4  4  1 1  4  2

2 2 2 2 3  1 3 3

4  1 4 4 1 4  1

3  2 1 1 3 1 2 4 4

4 1  4  1 5 3

3  2 2  2  4

1 4  3 4 3  2

3 3 2 4 2  2

4 1  3 4 3 1 2 4


How many numbers are lower than 5

3 2 5 2 6 6 2 4 2 3
2 2 6 6 3 6 6 1 6 4
2 2 6 3 2 6 4 5 3 3
1 1 2
Mathematics
Step-by-step answer
P Answered by Master

F=\frac{s^2_1}{s^2_2}=\frac{0.2211^2}{0.0768^2}=8.28

p_v =2*P(F_{24,21}8.28)=7.22x10^{-6}

Since the p_v < \alpha we have enough evidence to reject the null hypothesis. And we can say that we have enough evidence to conclude that the variation between the two machines is significant at 5% of significance.  

Step-by-step explanation:

Data given and notation  

Machine 1: 2.95 3.45 3.50 3.75 3.48 3.26 3.33 3.20 3.16 3.20 3.22 3.38 3.90 3.36 3.25 3.28 3.20 3.22 2.98 3.45 3.70 3.34 3.18 3.35 3.12

Machine 2: 3.22 3.30 3.34 3.28 3.29 3.25 3.30 3.27 3.38 3.34 3.35 3.19 3.35 3.05 3.36 3.28 3.30 3.28 3.30 3.20 3.16 3.33

n_1 = 23 represent the sampe size for machine 1

n_2 =22 represent the sample size for machine 2

\bar X_1 =3.33 represent the sample mean for machine 1

\bar X_2 =3.28 represent the sample mean for machine 2

s_1 = 0.2211 represent the sample deviation for machine 1

s^2_1 = 0.049 represent the sample variance for machine 1

s_2 = 0.0768 represent the sample deviation for machine 2

s^2_2 = 0.00690 represent the sample variance for machine 2

\alpha=0.05 represent the significance level provided

Confidence =0.95 or 95%

F test is a statistical test that uses a F Statistic to compare two population variances, with the sample deviations s1 and s2. The F statistic is always positive number since the variance it's always higher than 0. The statistic is given by:

F=\frac{s^2_1}{s^2_2}

Solution to the problem  

System of hypothesis

We want to determine whether there is a significant difference between thevariances in the bag weights for the two machines , so the system of hypothesis are:

H0: \sigma^2_1 = \sigma^2_2

H1: \sigma^2_1 \neq \sigma^2_2

Calculate the statistic

Now we can calculate the statistic like this:

F=\frac{s^2_1}{s^2_2}=\frac{0.2211^2}{0.0768^2}=8.28

Now we can calculate the p value but first we need to calculate the degrees of freedom for the statistic. For the numerator we have n_1 -1 =25-1=24 and for the denominator we have n_2 -1 =22-1=21 and the F statistic have 24 degrees of freedom for the numerator and 21 for the denominator. And the P value is given by:

P value

p_v =2*P(F_{24,21}8.28)=7.22x10^{-6}

And we can use the following excel code to find the p value:"=2*(1-F.DIST(8.2838,24,21,TRUE))"

Conclusion

Since the p_v < \alpha we have enough evidence to reject the null hypothesis. And we can say that we have enough evidence to conclude that the variation between the two machines is significant at 5% of significance.  

Mathematics
Step-by-step answer
P Answered by PhD

0.128 ; 0.872 ; 0.748 ; 0.124 ; 0.252

Step-by-step explanation:

Given the data above ;

The frequency distribution generated for the number of defects observed on each of 250 lcd screens are as follows :

__number of defects___frequency

0 24

1 82

2 38

3 43

4 31

5 26

6 6

A.) . What proportion of the screens have more than 4 defects? Give your answer to three decimal places.

More than 4 defects = (number of 5 defects + 6 defects) / total number of defects)

(26 + 6) / 250 = 32 / 250 = 0.128

b. What propotion of the screens have at most 4 defects? Give your answer to three decimal places.

Number of (0 + 1 + 2 + 3 + 4) defects

= (24 + 82 + 38 + 43 + 31) / 250

= 218 / 250 = 0.872

c. What proportion of the screens have fewer than 4 defects? Give your answer to three decimal places.

Number of (0 + 1 + 2 + 3) defects

= (24 + 82 + 38 + 43) / 250

= 187 / 250 = 0.748

d. What proportion of the screens have exactly 4 defects? Give your answer to three decimal places.

Number of 4 defects = 31

= 31 / 250

= 0.124

e. What proportion of the screens have at least 4 defects? Give your answer to three decimal places.

Number of (4 + 5 + 6) defects

= (31 + 26 + 6) / 250

= 63 / 250

= 0.252

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