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Previously, an organization reported that teenagers spent $4.5$hours per week, on average, on the phone. The organization thinks that, currently, the mean is higher. Fifteen randomly chosen teenagers were asked how many hours per week they spend on the phone. The sample mean was $4.75$hours with a sample standard deviation of $2.0$. Conduct a hypothesis test.

At a significance level of $a=0.05$, what is the correct conclusion?

a. There is enough evidence to conclude that the mean number of hours is more than$4.75$

b. There is enough evidence to conclude that the mean number of hours is more than 4.5

c. There is not enough evidence to conclude that the mean number of hours is more than 4.5

d. There is not enough evidence to conclude that the mean number of hours is more than 4.75

Instructions: For the following ten exercises,

Hypothesis testing: For the following ten exercises, answer each question.

a. State the null and alternate hypothesis.

b. State the p-value.

c. State alpha.

d. What is your decision?

e. Write a conclusion.

f. Answer any other questions asked in the problem

According to the Center for Disease Control website, in 2011 at least 18% of high school students have smoked a cigarette. An Introduction to Statistics class in Davies County, KY conducted a hypothesis test at the local high school (a medium sized–approximately 1,200 students–small city demographic) to determine if the local high school’s percentage was lower. One hundred fifty students were chosen at random and surveyed. Of the 150 students surveyed, 82 have smoked. Use a significance level of 0.05 and using appropriate statistical evidence, conduct a hypothesis test and state the conclusions.

According to the Center for Disease Control website, in $2011$ at least$18\%$of high school students have smoked a cigarette. An Introduction to Statistics class in Davies County,KY conducted a hypothesis test at the local high school (a medium sized–approximately $1,200$ students–small city demographic) to determine if the local high school’s percentage was lower. One hundred fifty students were chosen at random and surveyed. Of the$150$ students surveyed, $82$have smoked. Use a significance level of $0.05$ and using appropriate statistical evidence, conduct a hypothesis test and state the conclusions.

Driver error can be listed as the cause of approximately 54% of all fatal auto accidents, according to the American Automobile Association. Thirty randomly selected fatal accidents are examined, and it is determined that 14 were caused by driver error. Using α = 0.05, is the AAA proportion accurate?

Driver error can be listed as the cause of approximately $54\%$of all fatal auto accidents, according to the American Automobile Association. Thirty randomly selected fatal accidents are examined, and it is determined that $14$were caused by driver error. Using $\mathrm{Î\pm }=0.05,$ is the AAA proportion accurate?

The mean price of mid-sized cars in a region is $32,000. A test is conducted to see if the claim is true. State the Type I and Type II errors in complete sentences.

The US Department of Energy reported that 51.7% of homes were heated by natural gas. A random sample of 221 homes in Kentucky found that 115 were heated by natural gas. Does the evidence support the claim for Kentucky at the α = 0.05 level in Kentucky? Are the results applicable across the country? Why?

The US Department of Energy reported that $51.7\%$ of homes were heated by natural gas. A random sample of $221$homes in Kentucky found that $115$ were heated by natural gas. Does the evidence support the claim for Kentucky at the $\mathrm{Î\pm }=0.05$ level in Kentucky? Are the results applicable across the country? Why?

For Americans using library services, the American Library Association claims that at most $67\%$ of patrons borrow books. The library director in Owensboro, Kentucky feels this is not true, so she asked a local college statistic class to conduct a survey. The class randomly selected $100$ patrons and found that $82$borrowed books. Did the class demonstrate that the percentage was higher in Owensboro, KY? Use $\mathrm{Î\pm }=0.01$ level of significance. What is the possible proportion of patrons that do borrow books from the Owensboro Library?

The Weather Underground reported that the mean amount of summer rainfall for the northeastern US is at least 11.52 inches. Ten cities in the northeast are randomly selected and the mean rainfall amount is calculated to be 7.42 inches with a standard deviation of 1.3 inches. At the α = 0.05 level, can it be concluded that the mean rainfall was below the reported average? What if α = 0.01? Assume the amount of summer rainfall follows a normal distribution.