hirty-seven percent of all Americans drink bottled water more than once a week (Natural resources Defense Council, December 4, 2015). Suppose you have been hired by the Natural Resources Defence Council to investigate bottled water consumption in St. Paul. You plan to select a sample of St. Paulites to estimate the proportion who drink bottled water more than once a week. Assume the popluation proportion of St. Paulites who drink bottled water more than once a week is 0.37, the same as the overall proportion of Americans who drink bottled water more than once a week. Use z-table. a. Suppose you select a sample of 540 St.Paulites. Show the sampling distribution of (to 4 decimals). E(p) = ______ σ = _ b. Based upon a sample of 540 St. Paulites, what is the probability that the sample proportion will be within 0.01 of the population proportion (to 4 decimals). probability = _ c. Suppose you select a sample of 150 St.Paulites. Show the sampling distribution of p (to 4 decimals). E(p) = _ σ = _ d. Based upon a smaller sample of only 150 St. Paulites, what is the probability that the sample proportion will be within 0.01 of the population proportion (to 4 decimals). probability = _ e. As measured by the increase in probability, how much do you gain in precision by taking the larger sample in parts (a) and (b) rather than the smaller sample in parts (c) and (d)? Reduced by _____ Have gain in precision by increasing the sample.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Thirty-seven percent of all Americans drink bottled water more than once a week (Natural resources Defense Council, December 4, 2015). Suppose you have been hired by the Natural Resources Defence Council to investigate bottled water consumption in St. Paul. You plan to select a sample of St. Paulites to estimate the proportion who drink bottled water more than once a week. Assume the popluation proportion of St. Paulites who drink bottled water more than once a week is 0.37, the same as the overall proportion of Americans who drink bottled water more than once a week. Use z-table.

a. Suppose you select a sample of 540 St.Paulites. Show the sampling distribution of (to 4 decimals).
E(p) = __________
σ = _________

b. Based upon a sample of 540 St. Paulites, what is the probability that the sample proportion will be within 0.01 of the population proportion (to 4 decimals).
probability = _________

c. Suppose you select a sample of 150 St.Paulites. Show the sampling distribution of p (to 4 decimals).
E(p) = _________
σ = _________

d. Based upon a smaller sample of only 150 St. Paulites, what is the probability that the sample proportion will be within 0.01 of the population proportion (to 4 decimals).
probability = _________

e. As measured by the increase in probability, how much do you gain in precision by taking the larger sample in parts (a) and (b) rather than the smaller sample in parts (c) and (d)?
Reduced by _________
Have gain in precision by increasing the sample.

### Bottled Water Consumption Study

Thirty-seven percent of all Americans drink bottled water more than once a week (Natural Resources Defense Council, December 4, 2015). Suppose you have been hired by the Natural Resources Defense Council to investigate bottled water consumption in St. Paul. You plan to select a sample of St. Paulites to estimate the proportion who drink bottled water more than once a week. Assume the population proportion of St. Paulites who drink bottled water more than once a week is 0.37, the same as the overall proportion of Americans who drink bottled water more than once a week. Use the z-table for calculations.

#### Tasks:

**a. Sampling Distribution of a Sample of 540 St. Paulites:**
- Calculate the expected value $E(\bar{p})$ and the standard deviation $\sigma_{\bar{p}}$ for a sample of 540. Input field provided for calculations.

**b. Probability Calculation for Sample of 540:**
- Determine the probability that the sample proportion will be within 0.01 of the population proportion, using a sample size of 540. Answer to be provided to four decimal places.

**c. Sampling Distribution of a Sample of 150 St. Paulites:**
- Calculate the expected value $E(\bar{p})$ and the standard deviation $\sigma_{\bar{p}}$ for a smaller sample of 150. Input field provided for calculations.

**d. Probability Calculation for Sample of 150:**
- Determine the probability that the sample proportion will be within 0.01 of the population proportion, using a sample size of 150. Answer to be provided to four decimal places.

**e. Precision Gain by Increasing Sample Size:**
- Evaluate the increase in precision achieved by using the larger sample size from parts (a) and (b), compared to the smaller sample from parts (c) and (d). Choices are provided to select whether the precision is "Reduced by" or if there is a "Gain in precision by increasing the sample."

Note: Red "X" and green checkmarks indicate incorrect and correct answers, respectively, for input fields and options provided.

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