Simplify the expression and find its value: (2x+0.5)^2–(2x

A researcher claims that the mean of the salaries of elementary school teachers is greater than the mean of the salaries of seco

Brut [27]

Answer:

$t=\frac{(48250-45630)}{\sqrt{\frac{3900^2}{26}+\frac{5530^2}{24}}}}=1.921$

$df=n_{A}+n_{B}-2=26+24-2=48$

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

$p_v =P(t_{(48)}>1.921)=0.0303$

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 we can conclude that the mean for elementary school teachers is significantly higher than the mean for secondary teachers at 5% of significance

Step-by-step explanation:

Data given and notation

$\bar X_{A}=48250$ represent the mean of elementary teachers

$\bar X_{B}=45630$ represent the mean for secondary teachers

$s_{A}=3900$ represent the sample standard deviation for elementary teacher

$s_{B}=5530$ represent the sample standard deviation for secondary teachers

$n_{A}=26$ sample size selected

$n_{B}=24$ sample size selected

$\alpha=0.05$ 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 of the salaries of elementary school teachers is greater than the mean of the salaries of secondary school teachers, the system of hypothesis would be:

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

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

We don't know the population deviations, so for this case is better apply a t test to compare means, and the statistic is given by:

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

t-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".

Calculate the statistic

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

$t=\frac{(48250-45630)}{\sqrt{\frac{3900^2}{26}+\frac{5530^2}{24}}}}=1.921$

P-value

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

$df=n_{A}+n_{B}-2=26+24-2=48$

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

$p_v =P(t_{(48)}>1.921)=0.0303$

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 we can conclude that the mean for elementary school teachers is significantly higher than the mean for secondary teachers at 5% of significance

5 0

2 years ago

Ln how many ways 5 person sitted in a round table having 8 seats?

kvasek [131]

Answer: First consider the case that ‘just’ 5 persons are seated around a round table.

Clearly, ‘just’ 5 persons can be seated around a round table in (5 - 1)! = 4! = 24 ways.

Now, one vacant chair is to be inserted among them.

Say, for a particular sitting arrangement ‘ABCDE’; there are 5 scopes available for inserting the vacant chair - between A and B, between B and C, between C and D, between D and E & between E and A.

So, there are 5*24 = 120 ways available that 5 persons can sit around a round table with 6 chairs.

Step-by-step explanation:

First consider the case that ‘just’ 5 persons are seated around a round table.

Clearly, ‘just’ 5 persons can be seated around a round table in (5 - 1)! = 4! = 24 ways.

Now, one vacant chair is to be inserted among them.

Say, for a particular sitting arrangement ‘ABCDE’; there are 5 scopes available for inserting the vacant chair - between A and B, between B and C, between C and D, between D and E & between E and A.

So, there are 5*24 = 120 ways available that 5 persons can sit around a round table with 6 chairs.

5 0

2 years ago

Carrie has a stamp collection she is very proud of. She buys a frame to display her favorite stamps. The frame is 6 inches wide,

olga55 [171]

The stamps should be .85 inches each

7 0

2 years ago

Please help on 8-9 I'm desperate :/

slava [35]

8. 20-11+m

9. 30-17=h

Hope you get an A+

7 0

3 years ago

Regan cycles 78 miles in 6 hours.

Brut [27]

Answer:

12 mph

Step-by-step explanation:

First 30 miles while cycling at 15 mph. This means he spent 2 hours here.

Thus the 4 hours on the last 48 miles.

Average speed = distance / time

Average speed = 48 miles / 4 hours

Average speed = 12 mph

Therefore Regan's average speed is 12 mph for the last 48 miles.

4 0

2 years ago

Simplify the expression and find its value: (2x+0.5)^2–(2x–0.5)^2 for x=−3.5