Which distribution should you use for this problem? (Enter your answer in the fo

Question

Which distribution should you use for this problem? (Enter your answer in the form z or ta where df is the degrees of freedom.) r13 Explain your choice. The Student's t-distribution for 13 degrees of freedom should be used because we do not know the population standard deviation. O The standard normal distribution should be used because the sample standard deviation is known. O The Student's t-distribution for 14 degrees of freedom should be used because the sample standard deviation is known. The standard normal distribution should be used because the population standard deviation is known. Part (e) Construct a 99% confidence interval for the population mean length of time using training wheels. i) State the confidence interval. (Round your answers to two decimal places.) (ii) Sketch the graph. (Round your answers to two decimal places. Enter your a2 to three decimal places.) (ii) Calculate the error bound. (Round your answer to two decimal places.) Part () why would the error bound change if the confidence level were lowered to 90%? O When the confidence level increases, the error bound for the confidence interval ncreases as wel O When the confidence level changes, the interval does not change. O When the confidence level decreases, the error bound for the confidence interval O When the confidence level decreases, the error bound for the confidence interval decreases as well. O When the confidence level increases, the error bound for the confidence interval

Explanation / Answer

The T distribution (also called Student’s T Distribution) is a family of distributions that look almost identical to the normal distribution curve, only a bit shorter and fatter. The t distribution is used instead of the normal distribution when you have small samples (n<=30). The larger the sample size, the more the t distribution looks like the normal distribution.

When you look at the t-distribution tables, you’ll see that you need to know the “df.” This means “degrees of freedom” and is just the sample size minus one.

Step 1: Subtract one from your sample size. This will be your degrees of freedom.
Step 2: Look up the df in the left hand side of the t-distribution table. Locate the column under your alpha level

Sample Size: 14
Sample Mean: 6
Standard Deviation: 4
Confidence Level: 99%

Degrees of freedom =14-1=13

alpha=0.01

alpha/2=0.005,

t value at 0.005 which is at ±3.01

Standard error= s.d/41/2 =4/2=2

99% Confidence Interval: mean± talpha*(S.D/n1/2)

=6 ± 3.01*2
(-0.02 to 12.02)

"With 99% confidence the population mean is between (-0.02 to 12.02), based on only 14 samples."

error bound: ±6.02

Apparently a narrow confidence interval implies that there is a smaller chance of obtaining an observation within that interval, therefore, our accuracy is higher. Also a 95% confidence interval is narrower than a 99% confidence interval which is wider. The 99% confidence interval is more accurate than the 95%.

so when confidence interval is decreased it reduces the coverage of the area of the graph the mean is expected to be in and hence the value of error bound.

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