Question

pahntoms Redwood trees are the tallest plants on Earth. California is famous for its giant Redwood trees. But just how tall are they? A random sample of 47 California Redwood trees was taken and their heights measured. (This was not easy by the way.) The sample mean average height was 248 feet with a standard deviation of 26 feet. Does this data meet the assumptions necessary to perform a hypothesis test? If so, use a 5% significance level to test the claim that Redwood trees have an average height greater than 240 feet.

Answer 1

We conclude that the Redwood trees have an average height greater than 240 feet.

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.

Let
`\mu` = mean weight bag filling capacity of machine.

SO, Null Hypothesis,
`H_0` :
`\mu`
`\leq` 240 feet {means that the Redwood trees have an average height smaller than or equal to 240 feet}

Alternate Hypothesis,
`H_A` :
`\mu` > 240 feet {means that the Redwood trees have an average height greater than 240 feet}

The test statistics that will be used here is One-sample t test statistics as we don't know about the population standard deviation;

T.S. =
`(\bar X -\mu)/((s)/(√(n) ) )` ~
`t_n_-_1`

where,
`\bar X` = sample mean average height = 248 feet

s = sample standard deviation = 26 feet

n = sample of trees = 47

So, test statistics =
`(248-240)/((26)/(√(47) ) )` ~
`t_4_6`

= 2.109

Now at 5% significance level, the t table gives critical value of 1.6792 at 46 degree of freedom 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 we reject our null hypothesis.

Therefore, we conclude that the Redwood trees have an average height greater than 240 feet.