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kifflom [539]
3 years ago
13

How can you order rational numbers from least to greatest

Mathematics
2 answers:
Naily [24]3 years ago
7 0
<span><span>Find the highest and lowest terms </span></span>Figure out where your number line starts and ends. Put the lowest term on the far left and the highest term on the far right. Remember, negative numbers are lower than positive numbers, and the greater a negative number's distance from zero, the lower it is.
Mumz [18]3 years ago
7 0

Answer:

Step-by-step explanation:

Rational numbers are the numbers that can be expressed in  the form of fraction and the denominator cannot be equal to zero.

If we want to order rational numbers from least to greatest we can follow the following steps:

  • Take the lowest common multiple of all the denominators
  • Now, we have equal denominators and different numerators
  • To arrange the rational number from least to greatest, we pick the fraction with smallest numerator and then arrange them in increasing order.
  • This, will give us fractions arranged in ascending order.
  • After that, we can reduce the fractions to the given form.
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Answer:

a) There is statistical evidence showing that Nike shoues get more than 1000 miles.

b) The p-value of t=1.84 and df=149 is P=0.034.

It represents the probability of getting this sample results if the population parameters are the ones from the null hypothesis.

In this case, the low p-value shows is rare to get a sample of n=150 and mean 1015 miles, if the population mean is 1000. This is evidence that the null hypothesis is not true.

c) There is no enough evidence to claim that Nike shoes outperform Adidas shoes by 15 miles.

d) The p-value for t=0.55 and 318 df is P=0.29.

This shows that there is a probability of P=0.29 of getting samples that show this difference if the statement of the null hypothesis is true.

Step-by-step explanation:

a) We have to perform a hypothesis test with the following hypothesis:

H_0: \mu\leq 1000\\\\H_a: \mu>1000

The level of significance is 0.05.

The sample mean is 1015 and the sample standard deviation is 100.

The degrees of freedom are df = 150-1 = 149.

The t-statistic is:

t=\frac{M-\mu}{s/\sqrt{n}}=\frac{1015-1000}{100/\sqrt{150}} =\frac{15}{8.165} =1.84

The critical value for t is t=1.66. As the t-statistic is bigger than the critical t, it falls in the rejection region. The null hypothesis is rejected.

There is statistical evidence showing that Nike shoues get more than 1000 miles.

b) The p-value of t=1.84 and df=149 is P=0.034.

It represents the probability of getting this sample results if the population parameters are the ones from the null hypothesis.

In this case, the low p-value shows is rare to get a sample of n=150 and mean 1015 miles, if the population mean is 1000. This is evidence that the null hypothesis is not true.

c) In this case, the null and alternative hypothesis are:

H_0: \mu_1-\mu_2\leq 15\\\\H_a: \mu_1-\mu_2>15

The significance level is 0.05.

The difference between sample means is:

M_d=1015-995=20

The standard deviation of the difference is:

\sigma=\sqrt{\frac{\sigma_1^2}{n_1}+\frac{\sigma_2^2}{n_2}}= \sqrt{\frac{100^2}{150}+\frac{50^2}{170}}= \sqrt{66.67+14.70}=9

The degrees of freedom are:

df=n_1+n_2-2=150+170-2=318

The critical value is t=1.65

The t-statistic is:

t=\frac{M_d-(\mu_1-\mu_2)}{\sigma} =\frac{20-15}{9}= \frac{5}{9}= 0.55

The value ot the t-statistic is lower than the critical value, so it lies within the acceptance region.

There is no enough evidence to claim that Nike shoes outperform Adidas shoes by 15 miles.

d) The p-value for t=0.55 and 318 df is P=0.29.

This shows that there is a probability of P=0.29 of getting samples that show this difference if the statement of the null hypothesis is true.

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