2. A student measured the mass and volume of three different-sized samples of sand. He then calculated the

Mathematics

1 answer:

Aleks04 [339]3 years ago

3 0

9514 1404 393

Answer:

we expect the results to have less spread

Step-by-step explanation:

The spread between the maximum and minimum is almost 1/3 of the average of those values (0.8 vs 2.6). We expect repeated measurements of the same physical value to be well within 5% of their mean if they are done carefully.

The investigation has errors because the spread is too great.

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a) The 99% confidence interval would be given by (24.409;24.979)

b) n=464

Step-by-step explanation:

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

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Part a

The confidence interval for the mean is given by the following formula:

$\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

$df=n-1=47-1=46$

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,46)".And we see that $t_{\alpha/2}=2.01$