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Alex_Xolod [135]
3 years ago
7

Five students visiting the student health center for a free dental examination during National Dental Hygiene Month were asked h

ow many months had passed since their last visit to a dentist. Their responses were as follows. 5 17 12 21 29 Assuming that these five students can be considered a random sample of all students participating in the free checkup program, construct a 95% confidence interval for the mean number of months elapsed since the last visit to a dentist for the population of students participating in the program. (Give the answer to two decimal places.)

Mathematics
1 answer:
Andrews [41]3 years ago
4 0

Answer:

[0.9 months, 32.69 months]

Step-by-step explanation:

The mean is

\bf \bar x=\frac{5+17+12+21+29}{5}=16.8

The standard deviation is

\bf s=\sqrt{\frac{(5-16.8)^2+(17-16.8)^2+(12-16.8)^2+(21-16.8)^2+(29-16.8)^2}{5}}=8.1092

Now, we have to find two values a and b such that the area under the Normal curve with mean 16.8 and standard deviation 8.1092 between a and b equals <em>95% = 0.95 </em>

Using a spreadsheet we find these values are

a = 0.906

b = 32.694

<h3>(See picture) </h3>

and our 95% confidence interval for the mean number of months elapsed since the last visit to a dentist for the population of students participating in the program rounded to two decimal places is

[0.9 months, 32.69 months]

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