2) What characteristics of the original sample make it inappropriate for us to u

Question

2) What characteristics of the original sample make it inappropriate for us to use a t procedure to make our confidence interval?

3) What is the standard deviation of your bootstrap distribution?

4) Using your answers above, what is your 95% confidence interval for µ?

5) Given your confidence interval, would you reject a claim that µ = $21,000, or would you fail to reject a claim that µ = $21,000. Carefully explain your reasoning and reference your interval in your explanation for full credit.

StatKey Confidence Interval for a Mean, Median, Std. Dev. Mustang Price (Price) Show Data Table Edit Data Upload File Change Column(s) Generate 1 Sample Generate 10 Samples Generate 100 Sam ples Generate 1000 SamplesReset Plot Bootstrap Dotplot of Mean Original Sample n = 25, mean = 15.98 median= 11.9, stdev = 11.114 15 samples 4000 mean = 15.968 std. error = 2.162 Left TailTwo-TaiRight Tail 80 10 60 10 30 0 Bootstrap Sample Show Data Table 40 n= 25, mean= 13.672 median = 11.9, stdev = 9.172 15 20 10 10 12 18 20 24 30 0 15.968 67

Explanation / Answer

2)

For using t procedure to make our confidence interval, one of the condition is that the sampling distribution is normal or nearly normal. We see that the mean (15.98) is much larger than the median (11.9) in the original sample .So, distribution is right skewed distribution and is inappropriate for us to use a t procedure to make our confidence interval.

3)

The standard deviation of bootstrap distribution is 9.172

4)

Z value for 95% confidence interval is 1.96

95% confidence interval for µ is

(15.968 - 1.96 * 2.162, 15.968 + 1.96 * 2.162)

(11.73048, 20.20552)

5)

If we assume that the mean is in thousands of dollars and 21 does not lie in the 95% confidence interval (11.73048, 20.20552), we reject the claim that µ = $21,000 as 95% of the samples will have the means in the range (11.73048, 20.20552).

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