Mathematics, 31.07.2020 04:01 ssollers

A group of students estimated the length of one minute without reference to a watch or clock, and the times (seconds) are listed below. Use a 0.01 significance level to test the claim that these times are from a population with a mean equal to 60 seconds. Does it appear that students are reasonably good at estimating one minute?

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Answer from: aroyalstudent

Complete Question

The complete question is shown on the first uploaded image

Yes the students are reasonably good at estimating one minute

Option A is correct

The test statistics is t = 0.354

Step-by-step explanation:

From the question we are told that

The set of data is

68, 82 , 38 , 62 , 41, 25 , 57 , 64, 67, 47, 61, 71, 91, 87, 64

The population mean is $\mu = 60$

The level of significance is given as $\alpha = 0.01$

The critical value for this level of significance obtained from the normal distribution table is

$Z_{\alpha } = 2.33$

The null hypothesis is

$H_o : \mu = 60 \ seconds$

The alternative hypothesis is

$Ha : \mu \ne 60 \ seconds$

Generally the sample mean is mathematically represented as

$\= x = \frac{\sum x_i }{n }$

where n = 15

$\= x = \frac{ 68+ 82 + 38 + 62 + 41+ 25 + 57 + 64+67+ 47+ 61+ 71+ 91+ 87+ 64}{15}$

$\= x = 61.67$

The standard deviation is mathematically represented as

$\sigma =\sqrt{ \frac{ \sum (x_i - \= x )^2}{n} }$

substituting values

$\sigma =\sqrt{ \frac{ \sum (68-61.67)^2 + ( 82-61.67 )^2 + (38 -61.67)^2 + 62-61.67)^2 + (41-61.67)^2 +(25-61.67)^2 +( 57+61.67)^2 }{15} }$ $\sqrt{ \frac{ ( \cdot \cdot + ( 64-61.67)^2 + (67-61.67)^2 +(47-61.67)^2 + (61-61.67)^2+ (71-61.67)^2 + (91 -61.67)^2+( 87-61.67)^2 + (64-61.67)^2}{15} }$ => $\sigma = 18.23$

The test statistics is evaluated as

$t = \frac{\= x - \mu }{ \frac{\sigma }{\sqrt{n} } }$

substituting values

$t = \frac{61.67 -60 }{ \frac{18.23 }{\sqrt{ 15} } }$

t = 0.354

Now comparing the statistics and the critical value of the level of significance we see that the the test statistics is less than the critical value

Hence the we fail to reject the null hypothesis which mean that these times are from a population with a mean equal to 60 seconds

So we can state that yes the students are reasonably good at estimating one minute given that the sample mean is not far from the population mean

A group of students estimated the length of one minute without reference to a watch or clock, and th

Answer from: Quest

you forgot the options, but i found them anyways, the correct answer is "john wilson believes that words and actions based on the intellect are superior to those based on emotions".

john wilson is depicted as an extremely intelligent man. the point of the excerpt is to make a sort of distinction between emotional and rational intelligence. he happens to have both attributes, but he clearly favors his intellectual gifts. at the same time, because of his religious background, he's a little bit conflicted with this and it makes him ashamed.

hope this !

Answer from: Quest

2 2/3 hours duhh silly

step-by-step explanation:

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