Question

The following data show the number of hours per day 12 adults spent in front of screens watching television – related content. Complete parts a) and b) below.

1.3 5.1 4.2 5.4 7.7 6.8 5.6 2.7 5.2 1.8 2.2 8.8

Construct a 99% confidence interval to estimate the average number of hours per day adults spend in front of screens watching television – related content.

a) The 99% confidence interval to estimate the average number of hours per day adults spend in front of screens watching television – related content is from __________ hours to __________ hours.

b) What assumptions need to be made about this populations?

can you please show all work, step by step. thank you

Answer 1

First, we need to calculate the mean and standard deviation

Since we know that

Where n is the number of data points

Now

and n = 12

This implies that

a)

Confidence interval(in %) = 99

Since we know that

Required confidence interval = (4.73-2.134, 4.73+2.134)

Required confidence interval = (2.596, 6.864)

The 99% confidence interval to estimate the average number of hours per day adults spend in front of screens watching television-related content is from 2.596 hours to 6.864 hours.

b) What assumptions need to be made about this populations

b)

we use t distribution in this problem instead of z distribution because the sample size (n = 12) is less than 30

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