Answer:
0.288 < p < 0.338
Step-by-step explanation:
We have 2331 adults polled and 730 said they believe in UFOs. We are to construct a 99% confidence interval for the population proportion. We are told to round to 3 decimal places as needed.
We need to find p-hat and q-hat
p-hat = 730/2331 = 0.313
q-hat = 1 - p-hat = 1 - 0.313 = 0.687
Since the sample size is greater than 30, we use a z-value for 99% confidence, which is 2.575
See attached photo for the construction of the confidence interval
Answer:
We conclude that the average height of hobbit is taller than Yoda.
Step-by-step explanation:
We are given that in the Star Wars franchise, Yoda stands at only 66 centimetres tall.
From a sample of 7 hobbits, you find their mean height = 80 cm with standard deviation s = 10.8 cm.
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<u><em>Let </em></u><u><em> = average height of hobbit.</em></u>
So, Null Hypothesis, :
66 cm {means that the average height of hobbit is shorter than or equal to Yoda}
Alternate Hypothesis, :
> 66 cm {means that the average height of hobbit is taller than Yoda}
The test statistics that would be used here <u>One-sample t test statistics</u> as we don't know about population standard deviation;
T.S. = ~
where, = sample mean height = 80 cm
s = sample standard deviation = 10.8 cm
n = sample of hobbits = 7
So, <u><em>test statistics</em></u> = ~
= 3.429
The value of t test statistics is 3.429.
<em>Now, at 0.01 significance level the t table gives critical value of 3.143 for right-tailed test. Since our test statistics is more than the critical value of t as 3.429 > 3.143, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which </em><em><u>we reject our null hypothesis</u></em><em>.</em>
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Therefore, we conclude that the average height of hobbit is taller than Yoda.