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Answer:
We conclude that the mean number of thunder days is less than 92.
Step-by-step explanation:
We are given that Historically, a certain region has experienced 92 thunder days annually.
Over the past fifteen years, the mean number of thunder days is 72 with a standard deviation of 38.
<u><em>Let </em></u><u><em> = mean number of thunder days.</em></u>
So, Null Hypothesis, :
92 days {means that the mean number of thunder days is more than or equal to 92}
Alternate Hypothesis, :
< 92 days {means that the mean number of thunder days is less than 92}
The test statistics that would be used here <u>One-sample t test statistics</u> as we don't know about the population standard deviation;
T.S. = ~
where, = sample mean number of thunder days = 72
s = sample standard deviation = 38
n = sample of years = 15
So, <u><em>test statistics</em></u> = ~
= -2.038
The value of z test statistics is -2.038.
Since, in the question we are not given with the level of significance so we assume it to be 5%. Now, at 5% significance level the t table gives critical value of -1.761 at 14 degree of freedom for left-tailed test.
Since our test statistics is less than the critical value of t as -2.038 < -1.761, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which <u>we reject our null hypothesis</u>.
Therefore, we conclude that the mean number of thunder days is less than 92.