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Answer :
a) The best estimate of the population mean is the sample mean, which is 55 pounds.
b) For a 98 percent confidence level and 15 degrees of freedom (n-1), the critical value is approximately 2.602.
c) The confidence interval to be approximately (41.796, 68.204).
d) Based on the 95 percent confidence interval, we can conclude that the population mean is likely to fall within the range of 41.796 to 68.204 pounds.
a. The best estimate of the population mean is the sample mean, which is 55 pounds.
b. To find the value of r for a 98 percent confidence interval, we need to determine the critical value. Since the sample size is small (n = 16) and the population standard deviation is unknown, we need to use the t-distribution. For a 98 percent confidence level and 15 degrees of freedom (n-1), the critical value is approximately 2.602.
c. To develop the 95 percent confidence interval for the population mean, we can use the formula:
CI = Sample Mean ± (t * s / √n)
where t is the critical value, s is the sample standard deviation, and n is the sample size.
Plugging in the values, we get:
CI = 55 ± (2.602 * 20 / √16)
Calculating this expression, we find the confidence interval to be approximately (41.796, 68.204).
d. Based on the 95 percent confidence interval, we can conclude that the population mean is likely to fall within the range of 41.796 to 68.204 pounds. Since the interval includes the value of 67 pounds, it is reasonable to say that the population mean could be 67 pounds. However, we cannot be certain as the confidence interval provides a range of values within which the true population mean is likely to fall.
In conclusion,
a) The best estimate of the population mean is the sample mean, which is 55 pounds.
b) For a 98 percent confidence level and 15 degrees of freedom (n-1), the critical value is approximately 2.602.
c) The confidence interval to be approximately (41.796, 68.204).
d) Based on the 95 percent confidence interval, we can conclude that the population mean is likely to fall within the range of 41.796 to 68.204 pounds.
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