Jordy was living in a third story apartment in his complex. Up there he was paying an annual renters insurance premium of $325.0
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Answer:
So on this case the 95% confidence interval would be given by (4.95;4.99)
Step-by-step explanation:
Previous concepts
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.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
represent the sample mean
population mean (variable of interest)
s=0.0461 represent the sample standard deviation
n=19 represent the sample size
Confidence interval
The confidence interval for the mean is given by the following formula:
(1)
In order to calculate the critical value we need to find first the degrees of freedom, given by:
Since the Confidence is 0.95 or 95%, the value of and
, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,18)".And we see that
Now we have everything in order to replace into formula (1):
So on this case the 95% confidence interval would be given by (4.95;4.99)
Answer:
Proportion of the students recalled more than 15 names is 91.77%.
Step-by-step explanation:
We are given that a researcher was interested in seeing how many names a class of 38 students could remember after playing a name game After playing the name game, the students were asked to recall as many first names of fellow students as possible.
The mean number of names recalled was 19.41 with a standard deviation of 3.17.
<em>Let X = number of names recalled</em>
SO, X ~ N()
The z-score probability distribution is given by ;
Z = ~ N(0,1)
where, = mean number of names recalled = 19.41
= standard deviation = 3.17
The Z-score measures how many standard deviations the measure is away from the mean. After finding the Z-score, we look at the z-score table and find the p-value (area) associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X.
Now, proportion of the students recalled more than 15 names is given by = P(X > 15 names)
P(X > 15) = P( >
) = P(Z > -1.39)
= P(Z < 1.39) = 0.9177 {using z table}
<em>Therefore, proportion of the students recalled more than 15 names is </em><em>91.77%.</em>