Statistics Questions & Answers

97. How often do people who live near the beach actually visit the beach? A random sample of 25 residents in a coastal town revealed that the residents visited the beach 28.1 days a year on average. The standard deviation of the sample is 5.5 days. We wish to use the data to estimate the average number of days a year that all coastal dwellers visit the beach. (a) Find the point estimate for the mean number of days at the beach. (b) What is the standard error for the sample mean? (c) Find the multiplier for a \( 95 \% \) confidence interval for the mean. (d) State the margin of error. (e) Construct and interpret the \( 95 \% \) confidence interval for the mean number of days coastal dwellers visit the beach each year.

What is the mean of the data set rounded to the nearest tenth? \[ \begin{array}{llllllll}0.7 & 1.1 & 0.8 & 1.6 & 1.6 & 2.2 & 1.1\end{array} \]

What is the mean of the data set rounded to the nearest tenth? \[ \begin{array}{lllllll}0.7 & 1.1 & 0.8 & 1.6 & 1.6 & 2.2 & 1.1\end{array} \]

6. The distribution of pH measurements at a particular site is strongly skewed with mean 6.4 and standard deviation 0.1 . (a) What is the probability that an individual measurement yields a pH less than 6.35 ? (b) What is the probability that the mean of 40 measurements is less than 6.35 ?

Sunshine City was designed to attract retired people, and its current population of 50,000 residents has a mean age of 60 years and a standard deviation of 16 years. The distribution of ages is skewed to the left. (a) What is the distribution of the sample mean age of residents for a random sample of 100 residents? (b) What is the probability that a random sample of 100 residents have a mean age between 50 and 70 years of age? (c) What is the probability that the mean age of a random sample of 100 residents is less than 55 ?

3. Dados: \( U=\{1,2,3,4,5,6,7,8,9,10\}, A=\{1,3,6,8,10\}, B=\{2,4 \), \( 5,6,8\} \) y \( C=\{1,4,6,10\} \) halle: \( \begin{array}{ll}\text { a) } A \cup B & \text { b) } A \cap B \\ \text { c) }(A \cap B)^{\prime} & \text { d) }(A \cup C) \\ \text { e) }(A \cap B) \cup C & \text { f) }(A \cup B) \cap C\end{array} \)

The on-campus housing costs for a semester at a state university are Normally distributed with a mean of \( \$ 5800 \) and a standard deviation of \( \$ 750 \). (a) What is the distribution of the mean on-campus housing cost for a semester at this university for a random sample of 50 students? (b) What is the probability that a randomly selected on-campus student spends more than \( \$ 5000 \) per semester? (c) What is the probability that a random sample of 50 students spends an average of less than \( \$ 6000 \) ? (d) What is the probability that a random sample of 50 students spends an average of \( \$ 5500 \) to \( \$ 6000 \) per semester?

In the largest clinical trial ever conducted, 401,974 children were randomly assigned to two groups. The treatment group consisted of 201,229 children given the Salk vaccine for polio, and the other 200,745 children were given a placebo. Among those in the treatment group, 33 developed polio, and among those in the placebo group, 115 developed polio. If we want to use the methods for testing a claim about two population proportions to test the claim that the rate of polio is less for children'given the Salk vaccine, are the requirements for a hypothesis test satisfied? Explain. Choose the correct answer below. A. The requirements are not satisfied; the difference between the rates of those that developed polio in the two groups is not statistically significant. B. The requirements are satisfied; the samples are simple random samples that are independent, and for each of the two groups, the number of successes is at least 5 and the number of failures is at least 5 . C. The requirements are satisifed; the samples are simple random samples that are independent, and for each of the two groups, the sample size is at least 1000 . D. The requirements are not satisfied; the samples are not simple random samples that are independent.

93. In 2012, MetricNet found that the average length of a phone call to a help desk was about ten minutes. Call times were strongly right skewed with a standard deviation around 3.5 minutes. Suppose we take a random sample of 50 calls to the help desk and find the average \( (\bar{x}) \) call duration for the 50 calls. We repeat this process many times. (a) What do you expect the mean of the \( \bar{x} \) 's to be? (b) What do you expect the standard deviation of the \( \bar{x} \) 's to be? (c) What do you expect the shape of the \( \bar{x} \) 's to be? What guarantees this fact?

1. If we are interested in summarizing a variable with the mean, are we dealing with categorical or quantitative data? 2. In a few sentences, describe what the sampling distribution of the mean represents in your own words.