Answer :
Final answer:
To compute a 98% confidence interval for the mean pounds of trash generated per person in the city per week, use the t-distribution formula. The result gives us that the population mean is between 35.212 pounds and 38.188 pounds per week, with 98% confidence. If many groups of 172 members are sampled, about 2% of these confidence intervals will not contain the true population mean.
Explanation:
The subject of this question is about finding a 98% confidence interval in the field of statistics. First of all, to compute the confidence interval, you would use the t-distribution. The reason for this is because the population standard deviation is unknown and the sample size is less than 30.
To find the confidence interval, you multiply the standard error (standard deviation divided by the square root of your sample size) by the t-value. For a 98% confidence interval with 171 degrees of freedom (sample size - 1), the t-value is 2.611. So, the margin of error is calculated as 2.611* (7.5/sqrt(172)) = 1.488 pounds. Consequently, with 98% confidence the population mean number of pounds per person per week is between 36.7 - 1.488 and 36.7 + 1.488 pounds, or between 35.212 and 38.188 pounds.
Lastly, if many groups of 172 randomly selected members are studied, then a different confidence interval would be produced from each group. About 98 percent of these confidence intervals will contain the true population mean number of pounds of trash generated per person per week. Therefore, about 2 percent will not contain the true population mean. This is because a 98% confidence interval implies that we would expect 98 out of 100 of them to capture the population mean if we were to sample over and over again.
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