Which phrase has the same meaning as the expression below?

A random sample of n = 40 observations from a quantitative population produced a mean x = 2.2 and a standard deviation s = 0.29.

zmey [24]

Answer:

$t=\frac{2.2-2.1}{\frac{0.29}{\sqrt{40}}}=2.18$

$df=n-1=40-1=39$

Since is a one side test the p value would be:

$p_v =P(t_{(39)}>2.18)=0.0177$

If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and then the population mes seems to be higher than 2.1 at 5% of significance

Step-by-step explanation:

Data given and notation

$\bar X=2.2$ represent the sample mean

$s=0.29$ represent the sample standard deviation

$n=40$ sample size

$\mu_o =2.1$ represent the value that we want to test

$\alpha=0.05$ represent the significance level for the hypothesis test.

t would represent the statistic (variable of interest)

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

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the mean is higher than 2,1, the system of hypothesis would be:

Null hypothesis: $\mu \leq 2.1$

Alternative hypothesis: $\mu > 2.1$

If we analyze the size for the sample is > 30 but we don't know the population deviation so is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)

t-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".

Calculate the statistic

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

$t=\frac{2.2-2.1}{\frac{0.29}{\sqrt{40}}}=2.18$

P-value

The first step is calculate the degrees of freedom, on this case:

$df=n-1=40-1=39$

Since is a one side test the p value would be:

$p_v =P(t_{(39)}>2.18)=0.0177$

Conclusion

If we compare the p value and the significance level given $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and then the population mes seems to be higher than 2.1 at 5% of significance

7 0

3 years ago

Find the explicit formula for the sequence? -1,4,-16,64......

Ede4ka [16]

The explicit formula for given sequence is: $a_n = -1 . (-4)^{n-1}$

Step-by-step explanation:

Given sequence is:

-1,4,-16,64.....

We can see that there is no same difference between consecutive terms so we will find common ratio to see if it is a geometric sequence.

Here

$a_1 = -1\\a_2 = 4\\a_3 = -16\\a_4 = 64\\r = \frac{a_2}{a_1} = \frac{4}{-1} = -4\\r = \frac{a_3}{a_2} = \frac{-16}{4} = -4$

The explicit formula for geometric sequence is:

$a_n = a_1r^{n-1}$

Putting the values of r and a1

$a_n = -1 . (-4)^{n-1}$

Hence

The explicit formula for given sequence is: $a_n = -1 . (-4)^{n-1}$

Keywords: Geometric sequence, common ratio

Learn more about geometric sequence at:

#learnwithBrainly

5 0

3 years ago

Explain how to estimate 368 + 231 in two different ways

Komok [63]

First way. you could round to the tens place and add. 370 + 230 about 600.

round to the nearest hundreds. 400 plus 200. about 600.

3 0

2 years ago

Read 2 more answers

Write the explicit formula that represents the geometric sequence -2, 8, -32, 128

lora16 [44]

$a_{1}=-2 \\ \\ a_{2}=8 \\ \\ q= \frac{a_{2}}{a_{1}} \\ \\ q= \frac{8}{-2}=-4 \\ \\ a_{n}=a_{1}*q^{n-1} \\ \\ a_{n}=-2*-4^{n-1}$

7 0

2 years ago

Please answer the whole page .

baherus [9]

1. Brandi was driving 60mph down the highway. Ratio is 60/1. 60mi per 1 hr

2. Brandi bought 5 apples at the store and 6 oranges. The ratio of apples to oranges is 5:6 or 5 to 6.

3. Brandi has 3 sisters and 1 brother. Ratio of sisters to brothers is 3:1 or 3 to 1.

4. Brandi has 20 shirts and 10 pants in her closet. The ratio of shirts to pants is 20:10 or 20 to 10.

5. Brandi has 12 boys in her class and 13 girls. The ratio of boys to girls is 12:13 or 12 to 13

Hope this helps:)

7 0

3 years ago