A study published in 1993 found that babies born at different times of the year may develop the ability to crawl at different ages! The author of the study suggested that these differences may be related to the temperature at the time the infant is 6 months old. (Benson and Janette, Infant Behavior and Development [1993]. The study found that 32 babies born in January crawled at an average age of 29.84 weeks, with a standard deviation of 7.08 weeks. Among 21 July babies, crawling ages averaged 33.64 weeks, with a standard deviation of 6.91 weeks. Is this difference significant?

Answers

Answer 1

Answer:

Answer:

$t=\frac{(29.84-33.64)-0}{\sqrt{(7.08^2)/(32)+(6.91^2)/(21)}}}=-1.939$

$p_v =2*P(t_(51)<-1.939)=0.0580$

Comparing the p value with the significance assumed $\alpha=0.01$ we see that $p_v>\alpha$ so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, and the difference between the two groups is NOT significantly different at 1% of significance.

Step-by-step explanation:

Data given

$\bar X_(1)=29.84$ represent the mean for sample January

$\bar X_(2)=33.64$ represent the mean for sample July

$s_(1)=7.08$ represent the sample standard deviation for 1

$s_(2)=6.91$ represent the sample standard deviation for 2

$n_(1)=32$ sample size for the group 2

$n_(2)=21$ sample size for the group 2

$\alpha=0.01$ Significance level provided

t would represent the statistic (variable of interest)

Concepts and formulas to use

We need to conduct a hypothesis in order to check if the difference in the population means, the system of hypothesis would be:

Null hypothesis: $\mu_(1)-\mu_(2)=0$

Alternative hypothesis: $\mu_(1) - \mu_(2)\neq 0$

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

$t=\frac{(\bar X_(1)-\bar X_(2))-\Delta}{\sqrt{(\sigma^2_(1))/(n_(1))+(\sigma^2_(2))/(n_(2))}}$ (1)

And the degrees of freedom are given by $df=n_1 +n_2 -2=32+21-2=51$

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.

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

$t=\frac{(29.84-33.64)-0}{\sqrt{(7.08^2)/(32)+(6.91^2)/(21)}}}=-1.939$

P value

Since is a bilateral test the p value would be:

$p_v =2*P(t_(51)<-1.939)=0.0580$

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Select the PROPER Scientific Notation for the following value. 659,000,000,000 Question 1 options: 659 × 109 65.9 × 1010 6.59 × 1011 0.659 × 1012

Answers

The proper notation may depend on where you are. In the US, we like there to be one non-zero digit to the left of the decimal point, hence the appropriate form is ...

... 6.59×10¹¹

_____

Elsewhere, the "proper" form may require the first non-zero digit be placed to the right of the decimal point, as in 0.659×10¹². This is also the form used by some computer languages.

In Engineering usage, quite often the desired form is one that has the exponent be a multiple of 3, so the appropriate forms would be 659×10⁹ or 0.659×10¹².

Sometimes when you're doing problems using numbers in scientific notation, it can be convenient to scale the operands so the result comes out with no need for rescaling. For example, if you were to divide 100 by this number, you might write ...

... 100/(65.9×10¹⁰) ≈ 1.517×10⁻¹⁰

Without this "pre-scaling", you would get

... (10²)/(6.59×10¹¹) ≈ 0.1517×10⁻⁹ = 1.517×10⁻¹⁰

which requires rescaling the answer.

How many equations can you write that will equal 100

Answers

Step-by-step explanation:

Infinitely many equations can be written that will be equal to 100.

x + y = 100

2x - y = 100

and many more..

Solve the differential equation x^2 y"-xy' +y 0

Answers

Answer:

$y(x)\ =\ √(x)[C_1cos(√(3))/(2)logx+C_2sin(√(3))/(2)logx]$

Step-by-step explanation:

Given differential equation is

$x^2y$ (1)

Let's assume that

$x=e^t$

$=>\ t\ =\ logx$

then,

$(dx)/(dt)=e^t$

$and\ (d^2x)/(dt^2)=e^t$

We can write,

$(dy)/(dx)=(dy)/(dt).(dt)/(dx)$

$=e^(-t)(dy)/(dt)$

Similarly,

$(d^2y)/(dt^2)=(d^2y)/(dt^2).(dt^2)/(dx^2)$

$=e^(-2t).(d^2y)/(dt^2)$

Putting these values in equation (1), we will get

$e^(2t).e^(-2t).(d^y)/(dt^2)-e^t.e^(-t)(dy)/(dt)+y=0$

$=>(d^2y)/(dt^2)-(dy)/(dt)+y=0$

So, the characteristics equation can be given as

$D^2-D+1=0$

$=>D\ =\ (1+√(1-4))/(2)\ or\ (1-1√(1-4))/(2)$

$=>D=\ (1)/(2)+i(√(3))/(2)\ or\ (1)/(2)-i(√(3))/(2)$

Hence, the general solution of the equation can be give by

$y(t)\ =\ e^{(t)/(2)}[C_1cos(√(3))/(2)t+C_2sin(√(3))/(2)t]$

Now, by putting the value of t in above solution, we will have

$y(x)\ =\ e^{(1)/(2)logx}[C_1cos(√(3))/(2)logx+C_2sin(√(3))/(2)logx]$

$y(x)=\ √(x)[C_1cos(√(3))/(2)logx+C_2sin(√(3))/(2)logx]$

Hence, the solution of above given differential equation can be given by

$y(x)=\ √(x)[C_1cos(√(3))/(2)logx+C_2sin(√(3))/(2)logx]$

What is the solution to 7.5d=2.5d

Answers

Answer:

d = 0

Step-by-step explanation:

To find the solution to the given equation, we must solve for d in the equation.

7.5d = 2.5d

Subtract 2.5d from both sides.

5d = 0

Divide both sides by 5.

d = 0

So the solution to the equation would be d = 0.

I hope this helps. Happy studying.

Final answer:

The provided equation 7.5d=2.5d seems to be flawed as these quantities cannot be equal unless the variable 'd' is zero. Please double-check the equation.

Explanation:

The equation given is 7.5d=2.5d. However, this equation cannot be correct as 7.5d and 2.5d cannot be equal unless the variable 'd' equals zero. It seems that there's a typo or mistake in the provided equation. The solution could not be found as the equation seems to be flawed. Please double-check the equation and make sure the coefficients (the numbers before the 'd') and the variable 'd' are correct.

Learn more about Mathematical Equation here:

brainly.com/question/29514785

#SPJ2

Hhgggfgn help hellp
me

Answers

Answer:

First one

Step-by-step explanation:

Answer:

Hey! No need to fret ok so you are doing 7/6 the answer is 1.16 what do we know about this that is true.

Step-by-step explanation:

You are correct only the sum which is 1.16 is irrational because the product of the numbers is rational. Hope I help have a good day please put me for brainliest Thank You!

The value of 33 + 42 = .

Answers

Answer:

Step-by-step explanation:

Answer:

Step-by-step explanation:

+42

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