Work out the value of x! Will award brainiest

A random sample of 100 people from City A has an average IQ of 120 with a SD of 18. Independently of this, a random sample of 15

Sloan [31]

Answer:

$z=\frac{(120-116)-0}{\sqrt{\frac{18^2}{100}+\frac{15^2}{150}}}}=1.837$

$p_v =P(z>1.837)=1-P(Z$

Comparing the p value with a significance level for example $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can say that the average IQ on city A is signficantly higher than city B at 5% of singificance.

Step-by-step explanation:

$\bar X_{A}=120$ represent the mean for sample 1

$\bar X_{B}=116$ represent the mean for sample 2

$s_{A}=18$ represent the sample standard deviation for 1

$s_{B}=15$ represent the sample standard deviation for 2

$n_{A}=100$ sample size for the group 2

$n_{B}=150$ sample size for the group 2

$\alpha$ Significance level provided

z would represent the statistic (variable of interest)

Concepts and formulas to use

We need to conduct a hypothesis in order to check if residents of City A smarter on average, the system of hypothesis would be:

Null hypothesis: $\mu_{A}-\mu_{B}\leq 0$

Alternative hypothesis: $\mu_{A} - \mu_{B}> 0$

We don't have the population standard deviation's, but the sample sizes are large enough we can apply a z test to compare means, and the statistic is given by:

$z=\frac{(\bar X_{A}-\bar X_{B})-\Delta}{\sqrt{\frac{s^2_{A}}{n_{A}}+\frac{s^2_{B}}{n_{B}}}}$ (1)

z-test: Is used to compare group means. Is one of the most common tests and is used to determine whether the means of two groups are equal to each other.

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

$z=\frac{(120-116)-0}{\sqrt{\frac{18^2}{100}+\frac{15^2}{150}}}}=1.837$

P value

Since is a one right tailed test the p value would be:

$p_v =P(z>1.837)=1-P(Z$

Comparing the p value with a significance level for example $\alpha=0.05$ we see that $p_v$ so we can conclude that we have enough evidence to reject the null hypothesis, and we can say that the average IQ on city A is signficantly higher than city B at 5% of singificance.

5 0

3 years ago

Lynne is 25 years old and starting and IRA (individual retirement account). She is going to invest $150 at the beginning of each

Yuri [45]

The future amount of Lynnes retirement account can be computed using the formula of amortization or annuity:
P = A[(1+i)^n-1)]/(i)
A= amortization
i= 5.5%
n = 40*12 = 480
Subsituting the variables in th formula, Future amount of Lynne in 40 years is equal to
P = $29,082.71

3 0

3 years ago

Read 2 more answers

If f(x)=6(x-2), find f(5)

Ne4ueva [31]

Answer:

f(5) = 6(5 - 2) = 6(3) = 18

Step-by-step explanation:

You're asked to "evaluate" f(x)=6(x-2) when x = 5.

To do this, replace both instances of x with 5: f(5) = 6(5 - 2) = 6(3) = 18

7 0

3 years ago

Read 2 more answers

A square has a side that measures 5.5 units. What is the area of a circle with a circumference that equals the perimeter of the

Alexeev081 [22]

Answer:

Answer choice A) About 38.47 square units

Step-by-step explanation:

Since all four sides of a square have the same length, the perimeter of a square is just 4 times one of the side lengths. The perimeter of the square and therefore the circumference of the circle is 5.5*4=22. The circumference of a circle is 2 times the radius multiplied by pi. The radius of this circle is therefore:

$\dfrac{22}{2\pi}\approx 3.503$

Since the area of a circle is $\pi r^2$ , the area of this circle is:

$\pi \cdot 3.503^2= 3.14\cdot 12.271\approx 38.47$

Hope this helps!

4 0

3 years ago

The sum of the first 21 terms of the progression, - 18, - 15,-12.....is?

katovenus [111]

You can just use the tn formula to solve this tn= t1 + (n-1)d

8 0

2 years ago