MATHEMATICS COLLEGE

Suppose you read online that children first count to 10 successfully when they are 32 months old, on average. You perform a hypothesis test evaluating whether the average age at which gifted children first count to 10 is different than the general average of 32 months. What is the p-value of the hypothesis test? Choose the closest answer.

Answers

Answer 1

Answer:

Answer:

$p_v =2*P(t_((35))<-1.822)=0.0885$

Step-by-step explanation:

Assuming this info from R

hist(gifted$count)

## Min. 1st Qu. Median Mean 3rd Qu. Max.

## 21.00 28.00 31.00 30.69 34.25 39.00

## Sd

## [1] 4.314887

Data given and notation

$\bar X=30.69$ represent the mean

$s=4.3149$ represent the sample standard deviation

$n=36$ sample size

$\mu_o =32$ represent the value that we want to test

$\alpha$ 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 different than 32, the system of hypothesis would be:

Null hypothesis: $\mu = 32$

Alternative hypothesis: $\mu \neq 32$

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:

$t=(\bar X-\mu_o)/((s)/(√(n)))$ (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:

$t=(30.69-32)/((4.3149)/(√(36)))=-1.822$

P-value

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

$df=n-1=36-1=35$

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

$p_v =2*P(t_((35))<-1.822)=0.0885$

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Write an equation in point-slope form for the line through the given point with the given slope.(8, –3); m = -1/4

Answers

Answer:

y+3 = -1/4(x-8)

Step-by-step explanation:

Point slope form is y-y1 = m(x-x1) where m is the slope and (x1-y1) is a point on the line

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In a survey of 125 people, it was found that 60 people like chocolate ice cream, 25 people like vanilla ice cream, and 20 people like both chocolate and vanilla ice cream. Create a Venn diagram to represent this data and answer the following questions: a) How many people like only chocolate ice cream? b) How many people like only vanilla ice cream? c) How many people don't like either chocolate or vanilla ice cream? d) How many people like either chocolate ice cream or vanilla ice cream or both?

Answers

To create a Venn diagram for this data, we need to represent the number of people who like chocolate ice cream, vanilla ice cream, and both.

Let's start by drawing two overlapping circles. The left circle represents chocolate ice cream, the right circle represents vanilla ice cream, and the overlapping region represents people who like both.

To find the number of people who like only chocolate ice cream (a), we subtract the number of people who like both from the total number of people who like chocolate ice cream. So, 60 - 20 = 40 people like only chocolate ice cream.

To find the number of people who like only vanilla ice cream (b), we subtract the number of people who like both from the total number of people who like vanilla ice cream. So, 25 - 20 = 5 people like only vanilla ice cream.

To find the number of people who don't like either chocolate or vanilla ice cream (c), we subtract the total number of people who like chocolate or vanilla ice cream from the total number of people surveyed. So, 125 - (60 + 25 - 20) = 60 people don't like either flavor.

To find the number of people who like either chocolate ice cream or vanilla ice cream or both (d), we add the number of people who like only chocolate ice cream, the number of people who like only vanilla ice cream, and the number of people who like both. So, 40 + 5 + 20 = 65 people like either chocolate ice cream or vanilla ice cream or both.

In summary:

a) 40 people like only chocolate ice cream.

b) 5 people like only vanilla ice cream.

c) 60 people don't like either chocolate or vanilla ice cream.

d) 65 people like either chocolate ice cream or vanilla ice cream or both.

IWhat is the sale price of a stereo that normally sells for $250.00 and is on sale for 10% off?

Answers

Answer:

$225.00

Step-by-step explanation

First, take the percentage and switch it to a decimal. 10%= 0.10

Next, take $250.00 and multiply that by 0.10. 250x0.10=25

Lastly, subtract 25 from 250. 250-25= 225.

So you’re final answer is $225.00 Hope this helped!

Answer:

$225

Step-by-step explanation:

To find the sale price you convert 10% to decimals so that is equal to .10. Then you multiply the .10 by the original price, and that equals $25. After you have to subtract the found price by original price (250-25) then that should give you $225.

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