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3 years ago

From least to greates -4 3/7, -4 5/6, -5 3/7, 4 2/7, 5 1/7

Mathematics

1 answer:

krok68 [10]3 years ago

4 0

Answer:

The least number is - 5 3/7.

Then in order we have - 4 5/6.

- 4 3/7

4 2/7

And the greatest is 5 1/7.

Step-by-step explanation:

1. Let's look for the least number of this set and then continue to order them until we find the greatest, this way:

The least number is - 5 3/7 because is the biggest negative number among the three given to us.

The second least number is - 4 5/6, that is < - 5 3/7 and > than - 4 3/7. Their whole number is the same but the fraction part is bigger: 5/6 > 3/7 or 0.83 > 0.42.

The third number is the only negative number remaining: - 4 3/7.

Now, the fourth term in order is 4 2/7, because it's < 5 1/7.

Finally, the greatest number of the set given to us is 5 1/7.

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For this case we can find the critical value with the significance level $\alpha=0.05$ and if we find in the right tail of the z distribution we got:

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Replacing we got:

$z=\frac{0.344 -0.27}{\sqrt{\frac{0.27(1-0.27)}{125}}}=1.86$

Since the calculated value is higher than the critical value we have enough evidence to reject the null hypothesis and we can conclude that the true proportion of households with one person is significantly higher than 0.27

Step-by-step explanation:

We have the following dataset given:

$X= 43$ represent the households consisted of one person

$n= 125$ represent the sample size

$\hat p= \frac{43}{125}= 0.344$ estimated proportion of households consisted of one person

We want to test the following hypothesis:

Null hypothesis: $p \leq 0.27$

Alternative hypothesis: $p>0.27$

And for this case we can find the critical value with the significance level $\alpha=0.05$ and if we find in the right tail of the z distribution we got:

$z_{\alpha}= 1.64$

The statistic is given by:

$z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}}$ (1)

Replacing we got:

$z=\frac{0.344 -0.27}{\sqrt{\frac{0.27(1-0.27)}{125}}}=1.86$

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