I need help with arithmetic and geometric sequences

Mathematics

1 answer:

Drupady [299]3 years ago

7 0

So basically an arithmetic sequence has a common difference, a number which is either added or subtracted at a constant rate (only that number). A geometric sequence is the ratio between two numbers, meaning they are either multiplied or divided by the same number. The sequence would be neither if it follows none of these patterns. So by this logic:

14. Arithmetic, 15. Geometric, 16. Neither, 17. Geometric

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The number 17 to the power of three over five can be written in the form a root of 17 to the power of b. What is the value of B?

sashaice [31]

We have the following expression:
17 ^ (3/5)
We rewrite the expression.
We have then:
a ^ root (17 ^ b)
Where, for this case:
a = 5
b = 3
Substituting:
5 ^ root (17 ^ 3)
Answer:
the value of B is:
b = 3

3 0

3 years ago

For the hypothesis test H0: μ = 10 against H1: μ >10 and variance known, calculate the Pvalue for each of the following test

Basile [38]

Answer:

a) $p_v =P(Z>2.05)=1-P(z$

b) $p_v =P(Z>-1.84)=1-P(z$

c) $p_v =P(Z>0.4)=1-P(z$

Step-by-step explanation:

Some previous concepts

The p-value is the probability of obtaining the observed results of a test, assuming that the null hypothesis is correct.

A z-test for one mean "is a hypothesis test that attempts to make a claim about the population mean(μ)".

The null hypothesis attempts "to show that no variation exists between variables or that a single variable is no different than its mean"

The alternative hypothesis "is the hypothesis used in hypothesis testing that is contrary to the null hypothesis"

Hypothesis

Null hypothesis: $\mu=10$

Alternative hypothesis: $\mu >10$

If the random variable is distributed like this: $X \sim N(\mu,\sigma)$

We assume that the variance is known so the correct test to apply here is the z test to compare means, the statistic is given by the following formula:

$z_o=\frac{\bar X -\mu}{\sigma}$

Since we have the values for the statistic already calculated we can calculate the p value using the following formulas:

Part a

$p_v =P(Z>2.05)=1-P(z$

And in order to find the answer using excel we can use the following code:

"=1-NORM.DIST(2.05,0,1,TRUE)"

Part b

$p_v =P(Z>-1.84)=1-P(z$

And in order to find the answer using excel we can use the following code:

"=1-NORM.DIST(-1.84,0,1,TRUE)"

Part c

$p_v =P(Z>0.4)=1-P(z$

And in order to find the answer using excel we can use the following code:

"=1-NORM.DIST(0.4,0,1,TRUE)"

Conclusions

If we use a reference value for the significance, let's say $\alpha=0.05$ . For part a the $p_v$ so then we can reject the null hypothesis at this significance level.