Based on the information given, it should be noted that a 95% confidence means we are at least 95% sure that the true value of proportion will lie in the interval.
<h3>
What does the confidence level mean?</h3>
When we repeat the sampling 100 times and draw a confidence Interval for each one of them, at least 95 confidence intervals will contain the true value of the proportion. This is what we mean by being 95% confident
Also, when we have a random sample of 5. It implies that the condition of randomness is met and they are independent as well. Since the sample size is very small, the condition of a large sample is not satisfied.
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Using the t-distribution, as we have the standard deviation for the sample, it is found that the 95% confidence interval for the number of units students in their college are enrolled in is (11.7, 12.7).
<h3>What is a t-distribution confidence interval?</h3>
The confidence interval is:
In which:
is the sample mean.
- s is the standard deviation for the sample.
The critical value, using a t-distribution calculator, for a two-tailed <em>95% confidence interval</em>, with 49 - 1 = <em>48 df</em>, is t = 2.0106.
Hence:
The 95% confidence interval for the number of units students in their college are enrolled in is (11.7, 12.7).
More can be learned about the t-distribution at brainly.com/question/16162795
Answer:
Since this is means data and we do not know the populations standard deviation, a t-interval
needs to be used. The justification is found in checking the conditions needed for a t-interval. The
problem stated it was a random sample so we will assume this is sufficient. Since the sample size is
slightly under 30, we will still check for the data being roughly normal. Either a boxplot or normal
probability plot would suffice. In both cases there is no reason to doubt the sample data are roughly
normally distributed so we can proceed to the calculations.
The interval would be (69, 76)
Explanation:
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Answer:
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