Question

1. A city official claims that the proportion of all commuters who are in favor of an expanded public transportation system is 50%. A newspaper conducts a survey to determine whether this proportion is different from 50%. Out of 225 randomly chosen commuters, the survey finds that 90 of them reply yes when asked if they support an expanded public transportation system. Test the official's claim at a = 0.05. 2. A survey of 225 randomly chosen commuters are asked if they support an expanded public transportation system. 90 said yes. Construct a 95% confidence interval for the proportion of all commuters who support expanded public transportation. 3. An industrial company claims that the mean pH level of the water in a nearby river is 6.8. You randomly select 19 water samples and measure the pH of each. The sample mean and the sample standard deviation are 6.7 and 0.24, respectively. Is there enough evidence at a = 0.05 to reject the claim that the pH level is 6.8? Assume a normally distributed population. 4. You want to estimate the mean pH level of the water in a nearby river. You randomly select 19 water samples and measure the pH of each. The sample mean is 6.7 and the sample standard deviation is 0.24. Construct a 95% confidence interval for the true mean pH level. 5. Explain how using the same sample data and level of significance to conduct a hypothesis test and to construct a confidence interval can lead to the same conclusion. Use your work in #1 - 4 to provide specific examples of the connections between hypothesis tests and confidence intervals.

i am specifically looking at 4 and 5

Answer 1

4)

We know that the 95% confidence interval for population mean is given by:

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