Answer:
We conclude that the Redwood trees have an average height greater than 240 feet.
Step-by-step explanation:
We are given that a random sample of 47 California Redwood trees was taken and their heights measured. The sample mean average height was 248 feet with a standard deviation of 26 feet.
We have to test the claim that Redwood trees have an average height greater than 240 feet.
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<u><em>Let </em></u><u><em> = mean weight bag filling capacity of machine.</em></u>
SO, Null Hypothesis, : 240 feet {means that the Redwood trees have an average height smaller than or equal to 240 feet}
Alternate Hypothesis, : > 240 feet {means that the Redwood trees have an average height greater than 240 feet}
The test statistics that will be used here is <u>One-sample t test statistics</u> as we don't know about the population standard deviation;
T.S. = ~
where, = sample mean average height = 248 feet
s = sample standard deviation = 26 feet
n = sample of trees = 47
So, <u><em>test statistics</em></u> = ~
= 2.109
<em>Now at 5% significance level, the t table gives </em><u><em>critical value of 1.6792 at 46 degree of freedom</em></u><em> for right-tailed test. Since our test statistics is higher than the critical value of t as 2.109 > 1.6792, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which </em><u><em>we reject our null hypothesis</em></u><em>.</em>
Therefore, we conclude that the Redwood trees have an average height greater than 240 feet.