Applications of Confidence Intervals in Statistics

This solution is for OPTION 1

Step 1

This is involving identification of the number of observations; n thereafter calculating its mean score; X-bar and finally, the standard deviation is also calculated; s. 

In Option 1;

Number of observations; n = 7

The mean is given by;

The standard deviation; s is calculated as follows;

Step 2

Here, involve deciding on which Confidence interval to use; 95% or 99% which are common. In this case, I have decided to use the 95% confidence interval. Here are the already known Z values for some of the common Confidence intervals; 

Step 3

This will involve using the Z value above to calculate the confidence interval whose formula is given as;

Where:

X  is the mean

Z  is the chosen Z-value from the table above

s  is the standard deviation

n  is the number of observations

Therefore, we have,

This indicates that, the mean number of times that adults go out for dinner each week is from -0.5259 to 4.1854 times. 

However, the "95%" conclude that 95% of the mean number of times that adults go out for dinner each week will include the true mean, but 5% won't, ( Salkind, 2016) .

Therefore, there is a 1-in-20 chance (5%) that the calculated Confidence Interval does NOT include the true mean.

References 

Salkind, N. J. (2016).  Statistics for people who (think they) hate statistics . Sage Publications.