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Alex787 [66]
3 years ago
6

A random sample of 49 measurements from one population had a sample mean of 15, with sample standard deviation 5. An independent

random sample of 64 measurements from a second population had a sample mean of 18, with sample standard deviation 6. Test the claim that the population means are different. Use level of significance 0.01
Mathematics
1 answer:
kotykmax [81]3 years ago
7 0

Answer:

Comparing the p value with the significance level \alpha=0.01 we see that p_v so we can conclude that we have enough evidence to reject the null hypothesis, and the difference between the two groups is significantly different.  

Step-by-step explanation:

\bar X_{1}=15 represent the mean for sample 1

\bar X_{2}=18 represent the mean for sample 2

s_{1}=5 represent the sample standard deviation for 1  

s_{f}=6 represent the sample standard deviation for 2  

n_{1}=49 sample size for the group 2  

n_{2}=64 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{\frac{s^2_{1}}{n_{1}}+\frac{s^2_{2}}{n_{2}}}} (1)

And the degrees of freedom are given by df=n_1 +n_2 -2=49+64-2=111  

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{(15-18)-0}{\sqrt{\frac{5^2}{49}+\frac{6^2}{64}}}}=-2.897

P value

Since is a bilateral test the p value would be:  

p_v =2*P(t_{111}  

Comparing the p value with the significance level \alpha=0.01 we see that p_v so we can conclude that we have enough evidence to reject the null hypothesis, and the difference between the two groups is significantly different.  

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murzikaleks [220]

Answer:

The statements are incorrect as: The sum of even numbers from 1 to 100(i.e. 2550) is not double\twice of the sum of odd numbers from 1 to 100(i.e. 2500).

Step-by-step explanation:

We know that sum of an Arithmetic Progression(A.P.) is given by:

where 'n' denotes the "number" of digits whose sum is to be determined, 'a' denotes the first digit of the series and '' denote last digit of the series.

Now the sum of even numbers i.e. 2+4+6+8+....+100 is given by the use of sum of the arithmetic progression since the series is an A.P. with a common difference of 2.

image with explanation

Hence, sum of even numbers from 1 to 100 is 2550.

Also the series of odd numbers is an A.P. with a common difference of 2.

sum of odd numbers from 1 to 100 is given by: 1+3+5+....+99

.

Hence, the sum of all the odd numbers from 1 to 100 is 2500.

Clearly the sum of even numbers from 1 to 100(i.e. 2550) is not double of the sum of odd numbers from 1 to 100(i.e. 2500).

Hence the statement is incorrect.

Step-by-step explanation:

3 0
3 years ago
The answer isn’t C. Please help
anygoal [31]
Maybe the answers a?
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2 years ago
What is the value of the missing exponent?<br> 123,456,789 = 1.23456789 x 10^
mestny [16]

Answer:

123,456,789 = 1.23456789\times 10^8

Step-by-step explanation:

It is required to find the value of the missing exponent in the below value i.e.

123,456,789 = 1.23456789\times 10^x

Let the exponent is x.

Any number can be written in the scientific notation as :

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In this case, the decimal is applied before 8 numbers. It means that the value of x is 8.

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Answer:

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Step-by-step explanation:

( - 4) {}^{3}  =  ( - 4) \times ( - 4) \times ( - 4) =  - 64 \\

{4}^{ - 3}  =  (\frac{1}{4} ) {}^{3}  \\

({ \frac{1}{4} )}^{3}  =  \frac{1}{4}  \times  \frac{1}{4}  \times  \frac{1}{4}  =  \frac{1}{64}  \\

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