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A average amount of money on deposit in a savings account is $7500. Suppose a random sample of 49 accounts shows the average in

Valentin [98]

Answer:

z=-3.79

$p_v =2*P(z$

Step-by-step explanation:

1) Data given and notation

$\bar X=6850$ represent the mean average amount of money on deposit in savings account for the sample

$\sigma=1200$ represent the population standard deviation for the sample

$n=49$ sample size

$\mu_o =7500$ represent the value that we want to test

$\alpha=0.01$ represent the significance level for the hypothesis test.

z would represent the statistic (variable of interest)

$p_v$ represent the p value for the test (variable of interest)

2) State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean for the amount of money on deposit in savings account differs from 7500, the system of hypothesis would be:

Null hypothesis: $\mu =7500$

Alternative hypothesis: $\mu \neq 7500$

Since we know the population deviation, is better apply a z test to compare the actual mean to the reference value, and the statistic is given by:

$z=\frac{\bar X-\mu_o}{\frac{\sigma}{\sqrt{n}}}$ (1)

z-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".

3) Calculate the statistic

We can replace in formula (1) the info given like this:

$z=\frac{6850-7500}{\frac{1200}{\sqrt{49}}}=-3.79$

4)P-value

Since is a two-sided test the p value would be:

$p_v =2*P(z$

5) Conclusion

If we compare the p value and the significance level given $\alpha=0.01$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, so we can conclude that the average amount of money deposit in savings account its significantly different from 7500 tons at 1% of signficance.

7 0

4 years ago

What is the definition of present value?

Bezzdna [24]

Answer:

the value in the present of a sum of money, in contrast to some future value it will have when it has been invested at compound interest.

Step-by-step explanation:

6 0

3 years ago

Please need help on this

SashulF [63]

We can Notice that ∠ABC = ∠ACB

We know that if Two Angles are Equal then Angles Corresponding to those Sides are also Equal.

⇒ AB = AC

⇒ 4x + 4 = 6x - 14

⇒ 6x - 4x = 4 + 14

⇒ 2x = 18

⇒ x = 9

⇒ Length of BC = 2x + 7 = 2(9) + 7 = 18 + 7 = 25 units

4 0

3 years ago

1. A heterozygous white-fruited squash plant is crossed with a yellow-fruited plant, yielding 200 seeds. of these seeds, 110 pro

garri49 [273]

Answer:

Part 1 , not significant

Part II, significant

Step-by-step explanation:

Given that a heterozygous white-fruited squash plant is crossed with a yellow-fruited plant, yielding 200 seeds. of these seeds, 110 produce white-fruited plants while only 90 produce yellow-fruited plants

$H_0: Both colours are equally likely\\H_a: Both colours are not equally likely$

(Two tailed chi square test)

We assume H0 to be true and find out expected

If H0 is true expected would be 100 white and 100 yellow

Chi square = $\Sigma \frac{(O-E)^2}{E} \\=\frac{(110-100)^2}{100} +frac{(90-100)^2}{100} \\=2$

df = 1

p value = 0.152799

Since p value > 0.05 at 5% level we accept that the colours are equally likely

2)

Here observed are 1100 and 900

Expected 1000 & 1000

df = 1

Chi square = $\frac{20000}{100} =200$

p value <0.0001

These results are here statistically significant.

8 0

3 years ago

Last year the dept of the river was 4.2 feet deep. THIS YEAR UT DROPPED 11% find the depth of the f the river this year

Romashka [77]

Answer:

new depth =

4.2/100 X 89 = 3.738 feet

4 0

3 years ago