A public health official in St. Lucie county needs to estimate the average systolic blood pressure of all residents in St. Lucie county for a report that is being prepared for the Florida Department of Health. The official randomly selected 139 St. Lucie county residents and found that the mean systolic blood pressure of the sample was 124 millimeters of mercury (mm Hg). Using a 98% confidence level, determine the margin of error, E, and a confidence interval for the mean systolic blood pressure of all St. Lucie county residents. From past research, it is known that the standard deviation of the distribution of all St. Lucie county residents' systolic blood pressure is 15 mm Hg. Report the confidence interval using interval notation. Round solutions to two decimal places, if necessary. The margin of error is given by E=. A 98% confidence interval is given by

A filmologist is currently writing a report about feature films in the late 2010s. As a part of his research, the filmologist would like to estimate the mean length of feature films in the late 2010s. A random sample of 150 feature films from the 2010s was selected and the average of the sample was found to be 109 minutes. Suppose the standard deviation of the lengths of all feature films in the late 2010s is known to be 6.8 minutes. Find three different confidence intervals - one with a 98% confidence level, one with a 96% confidence level, and one with a 90% confidence level - for the average length of all feature films in the late 2010s. Notice how the confidence level affects the margin of error and the width of the interval. Report confidence interval solutions using interval notation. Round solutions to three decimal places, if necessary.

• The margin of error for a 98% confidence interval is given by E=. A 98% confidence interval is given by .
• The margin of error for a 96% confidence interval is given by E=. A 96% confidence interval is given by .
• The margin of error for a 90% confidence interval is given by E=. A 90% confidence interval is given by .

If the level of confidence is decreased, leaving all other characteristics constant, the margin of error of the confidence interval will Select an answer decrease increase . If the level of confidence is decreased, leaving all other characteristics constant, the width of the confidence interval will Select an answer decrease increase . Use the Student's t-distribution to find the t-value for each of the given scenarios. Round t-values to four decimal places.

• Find the value of t such that the area in the left tail of the t-distribution is 0.1, if the sample size is 102. t=
• Find the value of t such that the area in the right tail of the t-distribution is 0.025, if the sample size is 122. t=
• Find the value of t such that the area in the right tail of the t-distribution is 0.05, if the sample size is 97. t=
• Find the two values of tt such that 90% of the area under the tt-distribution is centered around the mean, if the sample size is 137. Enter the solutions using a comma-separated list. t=

A forester with the National Park Service was tasked with estimating the average age of the bald cypress trees (Taxodium distichum) in Big Cypress Swamp - a region in Everglades National Park. The forester extracted core samples from 39 randomly selected bald cypress trees in Big Cypress Swamp. The mean age of the sample was 325.9 years with a standard deviation of 23 years. Using a 80% confidence level, determine the margin of error, E, and a confidence interval for the average age of all bald cypress trees in Big Cypress Swamp. Report the confidence interval using interval notation. Round solutions to two decimal places, if necessary. The margin of error is given by E=. A 80% confidence interval is given by

An epidemiologist with the Florida Department of Health needs to estimate the proportion of Floridians who are infected with the corona virus but are asymptomatic (show no signs of the virus). The epidemiologist compiled a preliminary random sample of infected patients and found that 77% of the sample were also asymptomatic. How large a sample should be selected such that the margin of error of the estimate for a 90% confidence interval is at most 1.14%. Round the solution up to the nearest whole number. n=

An epidemiologist needs to estimate the proportion of residents of Okeechobee county that have been infected with COVID-19. Determine the most conservative estimate of the sample size required to limit the margin of error to within 0.027 of the population proportion for a 97% confidence interval. Round the solution up to the nearest whole number. n=

COVID-19 (novel corona virus) took the world by surprise in late 2019. By early 2020, nearly all countries worldwide were affected. Early reports have claimed that a large percentage of those infected with the corona virus were asymptomatic (showed no symptoms of the virus). The rate of asymptomatic infections is important, since such people can unwittingly spread the virus to those around them. Suppose the U.S. Centers for Disease Control and Prevention (CDC) needs to estimate the proportion of the infected population that is also asymptomatic. A random sample of 1030 infected patients is examined and 253 are observed to be asymptomatic. Determine the point estimate, p^ and the sample standard deviation, sp^. Round the sample proportion to four decimal places and round the standard deviation to six decimal places, if necessary. p^= sp= Using a 96% confidence level, determine the margin of error, E, and a confidence interval for the proportion of all patients who are infected with the corona virus and are also asymptomatic. Report the confidence interval using interval notation. Round solutions to four decimal places, if necessary. The margin of error is given by E=. A 96% confidence interval is given by .

The St. Lucie County Economic Development Board needs to estimate the proportion of all county residents who have earned at least a bachelor's degree. A random sample conducted by the St. Lucie County Economic Development Board found that 20.3% of all county residents held at least a bachelor's degree. Find three different confidence intervals - one with sample size 120, one with sample size 323, and one with sample size 782. Assume that 20.3% of the county residents in each sample have earned at least a bachelor's degree. Notice how the sample size affects the margin of error and the width of the interval. Report confidence interval solutions using interval notation. Report all solutions in percent form, rounded to two decimal places, if necessary.

• When n=120, the margin of error for a 99% confidence interval is given by . When n=120, a 99% confidence interval is given by .
• When n=323, the margin of error for a 99% confidence interval is given by . When n=323, a 99% confidence interval is given by .
• When n=782, the margin of error for a 99% confidence interval is given by . When n=782, a 99% confidence interval is given by .

If the sample size is increased, leaving all other characteristics constant, the margin of error of the confidence interval will Select an answer increase decrease . If the sample size is increased, leaving all other characteristics constant, the width of the confidence interval will Select an answer decrease increase .

Calculate the critical t-value(s) for each of the given hypothesis test scenarios below. If multiple critical values exist for a single scenario, enter the solutions using a comma-separated list. Round t-values to four decimal places.

• Find the critical t-value(s) for a left-tailed test of hypothesis for a mean, assuming the population standard deviation is unknown, with a sample size of 9, and let =0.01.
• Find the critical t-value(s) for a right-tailed test of hypothesis for a mean, assuming the population standard deviation is unknown, with a sample size of 82, and a significance level of 10%.
• Find the critical t-value(s) for a two-tailed test of hypothesis for a mean, assuming the population standard deviation is unknown, with a sample size of 25, and a significance level of 0.1%.
• Find the critical t-value(s) for a two-tailed test of hypothesis for a mean, assuming the population standard deviation is unknown, with a sample size of 94, and let =0.05.

1 Nine out of ten dentists recommend this toothpaste! You have certainly heard the above claim before. Advertisers frequently claim that some percentage of doctors or dentists recommend a given health product. It's best to take such claims with a large grain of salt. Suppose a recent advertisement claims that 9 out of 10 dentists (90%) recommend a certain brand of toothpaste. A consumer advocacy group is highly suspicious of this claim and randomly surveys 251 dentists. They find that 95.5% of the sample recommends the given brand of toothpaste. Using =0.05, test the hypothesis that the proportion of all dentists who recommend this brand of toothpaste is different than 90%. State the null and alternative hypothesis for this test. :H0:? = > < p = p p p p > p < :H1:? = > < p = p p p p > p < Determine if this test is left-tailed, right-tailed, or two-tailed.

• two-tailed
• right-tailed
• left-tailed

Should the standard normal (z) distribution or Student's (t) distribution be used for this test?

• The Student's t distribution should be used
• The standard normal (z) distribution should be used

Determine the critical value(s) for this hypothesis test. Round the solution(s) to two decimal places. If more than one critical value exists, enter the solutions using a comma-separated list. Determine the test statistic. Round the solution to two decimal places. Determine the appropriate conclusion for this hypothesis test.

• The sample data do not provide sufficient evidence to reject the null hypothesis that the proportion of all dentists that recommend this brand of toothpaste is 0.9 and thus we conclude that the proportion of dentists that recommend this brand of toothpaste is likely equal to 0.9.
• The sample data provide sufficient evidence to reject the alternative hypothesis that the proportion of dentists who recommend this brand of toothpaste is significantly different than 0.9 and thus we conclude that the proportion of all dentists that recommend this brand of toothpaste is likely equal to 0.9.
• The sample data provide sufficient evidence to reject the null hypothesis that the proportion of all dentists that recommend this brand of toothpaste is 0.9 and thus we conclude that the proportion of dentists that recommend this brand of toothpaste is not equal to 0.9.
• The sample data do not provide sufficient evidence to reject the alternative hypothesis that the proportion of dentists who recommend this brand of toothpaste is significantly different than 0.9 and thus we conclude that the proportion of all dentists that recommend this brand of toothpaste is likely different than 0.9.

An adviser in student services would like to estimate the average monthly car payment of all IRSC students. From past research, it is known that the standard deviation of the distribution of all IRSC student car payments is $49. Determine the sample size necessary such that the margin of error of the estimate for a 99% confidence interval for the average monthly car payment of all IRSC students is at most $3.60. Round the solution up to the nearest whole number. n=