Question

Say a town of 50 used to typically come into contact with 30 people a day, standard deviation of 20. They want to "social distance", so they reduce this number to 28 people a day. Is this significantly less than before at a 90% level?

Answer 1

The null and alternate hypothesis are:

H0:

Ha:

The test statistic is given by:

Since this is a left-tailed test, so the p-value is given by:

Here, the level of significance is

Since p-value is greater than 0.10, so we do not have sufficient evidence to reject the null hypothesis H0.

Thus we cannot conclude that that the number has significantly reduced.