A random sample of 15 adults living in a small town are...

A random sample of 15 adults living in a small town are selected to estimate the proportion of voters favoring a certain candidate for mayor. Each individual was also asked if he or she was a college graduate. Byletting $Y$ and $N$ designate the responses of "yes" and "no" to the education question, the following sequence was obtained: $$ N N N N Y Y N Y Y N Y \mathrm{~A}^{\prime \prime} N N N $$ Use the runs test at the 0.1 level of significance to determine if the sequence supports the contention that the sample was selected at random.

A random sample of 15 adults living in a small town are selected to estimate the proportion of voters favoring a certain candidate for mayor. Each individual was also asked if he or she was a college graduate. Byletting $Y$ and $N$ designate the responses of "yes" and "no" to the education question, the following sequence was obtained:
$$
N N N N Y Y N Y Y N Y \mathrm{~A}^{\prime \prime} N N N
$$
Use the runs test at the 0.1 level of significance to determine if the sequence supports the contention that the sample was selected at random.

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Random Sampling

Random sampling is the process by which every member of a population has an equal chance of being selected. This approach is fundamental to statistical inference as it helps ensure that the sample accurately represents the population, thereby minimizing selection bias.

Hypothesis Testing and Significance Level

Hypothesis testing is a statistical framework used to decide whether there is enough evidence in a sample to infer that a certain condition holds for the entire population. The significance level, such as 0.1, sets the threshold for rejecting the null hypothesis, indicating the probability of committing a Type I error if the null hypothesis is true.

Nonparametric Methods

Nonparametric statistical methods are techniques that do not assume a specific probability distribution in the data. They are particularly useful when the underlying distribution is unknown or when the data do not satisfy the assumptions required for parametric tests.

Runs Test

The runs test is a nonparametric method used to determine whether a sequence of categorical data (such as responses) occurs in a random order. By counting the number of runs, or uninterrupted sequences of similar items, the test assesses whether the order deviates from randomness.

Please give Ace some feedback