Previously, an organization reported that teenagers spent...

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.

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.

Key Concepts

Conclusion Formulation

Drawing conclusions in hypothesis testing means translating the statistical decision into a statement about the population parameter. This involves explaining whether the evidence was sufficient to support the claim made in the alternative hypothesis, and discussing the practical implications of the result.

Decision Rule

The decision rule in hypothesis testing involves comparing the p-value to the significance level. If the p-value is less than or equal to ?, the null hypothesis is rejected; if it is greater than ?, there is insufficient evidence to reject the null hypothesis.

Significance Level (?)

The significance level, often denoted as alpha (?), is the threshold for determining statistical significance. It represents the probability of rejecting the null hypothesis when it is actually true (Type I error), and is commonly set at values like 0.05 or 0.01.

Sample Statistics

Sample statistics, such as the sample mean and sample standard deviation, are calculated from data and are used to estimate population parameters. They are essential in hypothesis testing for computing the test statistic and making inferences about the population.

t-Test

A t-test is used when the sample size is small and the population standard deviation is unknown. It is used to compare the sample mean to a known or hypothesized population mean, and relies on the t-distribution for determining the probability of observing the sample mean given the null hypothesis.

Null and Alternative Hypotheses

The null hypothesis (H0) typically asserts that there is no difference or effect, while the alternative hypothesis (H1) asserts the presence of an effect or a difference in a specific direction. Clearly stating these hypotheses is crucial as they form the basis of the test and subsequent decision making.

Hypothesis Testing

Hypothesis testing is a statistical method used to make decisions or inferences about population parameters based on sample data. It involves formulating a null hypothesis that represents a default or no-effect situation and an alternative hypothesis that represents a new claim or effect, then determining whether the sample data provide sufficient evidence to reject the null hypothesis.

p-Value

The p-value measures the probability of obtaining a test statistic at least as extreme as the one observed, assuming the null hypothesis is true. It is compared against a significance level to decide whether to reject the null hypothesis; a small p-value indicates strong evidence against the null hypothesis.

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