Historically a certain region has experienced 68 thunder day

Historically, a certain region has experienced 68 thunder days annually. (A \"thunder day\" is day on which at least one instance of thunder is audible to a normal human ear). Over the past seven years, the mean number of thunder days is 58 with a standard deviation of 26. Can you conclude that the mean number of thunder days is less than 68? Use the level of significance.

Solution

The null hypothesis is that the mean number of thunder days is not less than 68 i.e., Ho: not < 68 against the alternative hypothesis is that the mean number of thunder days is less than 68 i.e., H1: < 68. Given that =68 & n= 68, xbar=58, =26, then Z=(xbar-)/(/n)=(58-68)/(26/68)=-3.1715. And the tabulated value of Z at 5% level of significance i.e., left tail test is -1.645, Zcal<Ztab, so we accept Ho, i.e., the mean number of thunder days is not less than 68.