The head of the Philippine University (PU) observes a decline on the alcoholic expenditures of leamers from a monthly expenditure of Php 350 pesos in the previous year. To check on this, he randomly selected 10 PU learners who drink alcoholic beverages and asked the amount, in pesos, that they usually spend on alcoholic beverages in a month. It is known that the usual amount spent on alcoholic beverages by learners who drink alcoholic beverages follows the normal distribution with standard deviation of Php 10. The data collected are: 400, 235, 200, 250, 200, 300, 500, 430, 420, and 220. 1. Construct and interpret a 95% confidence interval for the true mean amount spent by the learners on alcoholic beverages. 2. Find a 90% confidence interval for the true mean amount spent by the learners on alcoholic beverages. 3. Calculate the widths of the confidence intervals in (a) and (b). How was the width of the confidence interval affected by the decrease in the confidence coefficient holding the other factors constant? 4. How many leamers must be sampled in order to be 99% confident that the estimated mean amount spent on alcoholic beverages will be within Php 2.00 of the true mean?

MATLAB: An Introduction with Applications
6th Edition
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Author:Amos Gilat
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The head of the Philippine University (PU) observes a decline on the alcoholic expenditures of learners from a monthly expenditure of Php 350 pesos in the previous year. To check on this, he randomly selected 10 PU learners who drink alcoholic beverages and asked the amount, in pesos, that
they usually spend on alcoholic beverages in a month. It is known that the usual amount spent on alcoholic beverages by learners who drink alcoholic beverages follows the normal distribution with standard deviation of Php 10. The data collected are: 400, 235, 200, 250, 200, 300, 500, 430, 420,
and 220.
1. Construct and interpret a 95% confidence interval for the true mean amount spent by the learners on alcoholic beverages.
2. Find a 90% confidence interval for the true mean amount spent by the learners on alcoholic beverages.
3. Calculate the widths of the confidence intervals in (a) and (b). How was the width of the confidence interval affected by the decrease in the confidence coefficient holding the other factors constant?
4. How many learners must be sampled in order to be 99% confident that the estimated mean amount spent on alcoholic beverages will be within Php 2.00 of the true mean?
Transcribed Image Text:The head of the Philippine University (PU) observes a decline on the alcoholic expenditures of learners from a monthly expenditure of Php 350 pesos in the previous year. To check on this, he randomly selected 10 PU learners who drink alcoholic beverages and asked the amount, in pesos, that they usually spend on alcoholic beverages in a month. It is known that the usual amount spent on alcoholic beverages by learners who drink alcoholic beverages follows the normal distribution with standard deviation of Php 10. The data collected are: 400, 235, 200, 250, 200, 300, 500, 430, 420, and 220. 1. Construct and interpret a 95% confidence interval for the true mean amount spent by the learners on alcoholic beverages. 2. Find a 90% confidence interval for the true mean amount spent by the learners on alcoholic beverages. 3. Calculate the widths of the confidence intervals in (a) and (b). How was the width of the confidence interval affected by the decrease in the confidence coefficient holding the other factors constant? 4. How many learners must be sampled in order to be 99% confident that the estimated mean amount spent on alcoholic beverages will be within Php 2.00 of the true mean?
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