When factored into primes 2020=2^2*5^1*101^1.How many positive non-prime factors does 2020 have?

The standard deviation of math test scores at one high school is 16.1. A teacher claims that the standard deviation of the girls

Elanso [62]

Answer:

$\chi^2 =\frac{22-1}{259.21} 166.41 =13.482$

$p_v =P(\chi^2$

In order to find the p value we can use the following code in excel:

"=CHISQ.DIST(13.482,21,TRUE)"

If we compare the p value and the significance level provided we see that $p_v >\alpha$ so on this case we have enough evidence in order to FAIL reject the null hypothesis at the significance level provided. And that means that the population deviation is not significantly lower than 16.1 at 1% of significance.

Step-by-step explanation:

Notation and previous concepts

A chi-square test is "used to test if the variance of a population is equal to a specified value. This test can be either a two-sided test or a one-sided test. The two-sided version tests against the alternative that the true variance is either less than or greater than the specified value"

$n=22$ represent the sample size

$\alpha=0.01$ represent the confidence level

$s^2 =12.9^2=166.41$ represent the sample variance obtained

$\sigma^2_0 =16.1^2 =259.21$ represent the value that we want to test

Null and alternative hypothesis

On this case we want to check if the population deviation is smaller than 16.1 (that's equivalent to check if the population variance is lower than 259.21:

Null Hypothesis: $\sigma^2 \geq 259.21$

Alternative hypothesis: $\sigma^2$

Calculate the statistic

For this test we can use the following statistic:

$\chi^2 =\frac{n-1}{\sigma^2_0} s^2$

And this statistic is distributed chi square with n-1 degrees of freedom. We have eveything to replace.

$\chi^2 =\frac{22-1}{259.21} 166.41 =13.482$

Calculate the p value

In order to calculate the p value we need to have in count the degrees of freedom , on this case 21. And since is a left tailed test the p value would be given by:

$p_v =P(\chi^2$

In order to find the p value we can use the following code in excel:

"=CHISQ.DIST(13.482,21,TRUE)"

Conclusion

If we compare the p value and the significance level provided we see that $p_v >\alpha$ so on this case we have enough evidence in order to FAIL reject the null hypothesis at the significance level provided. And that means that the population deviation is not significantly lower than 16.1 at 1% of significance.

3 0

3 years ago

Can you help me solve an infinite geometric sequence

zaharov [31]

A geometric series like

$\displaystyle \sum_{n=1}^\infty \dfrac{1}{\alpha^n}$

Converges if and only if $|\alpha|>1$ . If this is the case, the sum equals

$\displaystyle \sum_{n=1}^\infty \dfrac{1}{\alpha^n} = \dfrac{1}{\alpha-1}$

So, in your case, you have convergence if and only if

$|2+a|>1 \iff 2+a>1 \lor 2+a-1 \lor a$

And if this is the case, the sum equals

$\displaystyle \sum_{n=1}^\infty \dfrac{1}{(2+a)^n} = \dfrac{1}{2+a-1} = \dfrac{1}{a+1}$

8 0

3 years ago

Could you explain how to do them? i have no idea what they were called

dimaraw [331]

Answer: See below.

Step-by-step explanation:

First table from left to right

7 12 14 11 6 8 13 12 9 15

Second table from left to right

1 9 6 12 7 8 5 9 4 3

Third table from left to right

12 33 21 15 24 36 9 27 6 18

Fourth table from left to right

2 5 9 6 12 3 8 7 11 10

Please leave mark this answer as brainliest if I helped you out :)

3 0

2 years ago

What is 3 1/8 - 1 7/8 = write your answer as a mixed number

S_A_V [24]

1 and 1/4

To get this final answer, follow these steps:

3 1/8 - 1 7/8

Change these into improper fractions:

25/8 - 15/8

Then subtract the numerators:

10/8

And finally, make it a mixed number and then simplify.

1 and 2/8 -> 1 1/4

Hope this helps!

5 0

3 years ago

Can you answer this question please?

RUDIKE [14]

To be honest not really

5 0

3 years ago