Mathematics, 21.12.2019 00:31 grandpianograce

Sacramento county high school seniors have an average sat score of 1,020. from a random sample of 144 sacramento high school students we find the average sat score to be 1,100 with a standard deviation of 144. we want to know if these high school students are representative of the overall population. what are our hypotheses?

Answers: 3

Show answers

Answers

We need to conduct a hypothesis in order to check if the high school students are representative of the overall population (or if the true mean is 1020 or not), the system of hypothesis would be:

Null hypothesis: $\mu = 1020$

Alternative hypothesis: $\mu \neq 1020$

Step-by-step explanation:

Previous concepts and data given

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X=1100$ represent the sample mean

s=144 represent the sample standard deviation

n=144 represent the sample selected

$\alpha$ significance level

State the null and alternative hypotheses.

We need to conduct a hypothesis in order to check if the high school students are representative of the overall population (or if the true mean is 1020 or not), the system of hypothesis would be:

Null hypothesis: $\mu = 1020$

Alternative hypothesis: $\mu \neq 1020$

If we analyze the size for the sample is > 30 and 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:

$t=\frac{1100-1020}{\frac{144}{\sqrt{144}}}=6.67$

P-value

First we need to calculate the degrees of freedom given by:

df=n-1=144-1 =143

Then since is a two sided test the p value would be:

$p_v =2*P(t_{144}6.67)=2.59x10^{-10}$

Conclusion

If we compare the p value and 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, so we can conclude that the population mean is significant different from 1020 at 5% of significance.

Answer from: Quest

This does not make sense

Answer from: Quest

step-by-step explanation:

if it takes 8 pounds to make 12 divide 12 by 8 and you get 1.5, 1.5 x 16 = 24

Another question on Mathematics

Mathematics, 21.06.2019 16:20

Giuseppi's pizza had orders for $931.00 of pizzas. the prices were $21 for a large pizza, 514 for a medium pizza, and $7 for a small pizza. the number of large pizzas was two less than four times the number of medium pizzas. thenumber of small pizzas was three more than three times the number of medium pizzas. how many of each size of pizza were ordered?

Answers: 1

Answer

Mathematics, 21.06.2019 19:00

Analyze the graph of the cube root function shown on the right to determine the transformations of the parent function. then, determine the values of a, h, and k in the general equation. y=a3x-h+k h= . k= done 000000l o 7 of 8

Answers: 2

Answer

Mathematics, 21.06.2019 20:30

What is the interquartile range of this data set? 2, 5, 9, 11, 18, 30, 42, 48, 55, 73, 81

Answers: 1

Answer

Mathematics, 21.06.2019 21:30

Aculture started with 4,000 bacteria. after 5 hours, it grew to 5,200 bacteria. predict how many bacteria will be present after 19 hours. round your answer to the nearest whole number.

Answers: 1

Answer

You know the right answer?

Sacramento county high school seniors have an average sat score of 1,020. from a random sample of 14...

Questions