It is believed that Lake Tahoe Community College (ITC)...

It is believed that Lake Tahoe Community College (ITC) Intermediate Algebra students get less than seven hours of sleep per night, on average. A survey of 22 LTCC Intermediate Algebra students students a mean of 7.24 hours with a standard deviation of 1.93 hours. At a level of significance of 5$\%$ , do LTCC Intermediate Algebra students get less than seven hours of sleep per night, on average? The Type II error is not to reject that the mean number of sleep LTCC students get per night is at lest seven when, in fact, the mean number of hours a. is more than seven hours. b. is at most seven hours. c. is at least seven hours. d. is less than seven hours.

It is believed that Lake Tahoe Community College (ITC) Intermediate Algebra students get less than seven hours of sleep per night, on average. A survey of 22 LTCC Intermediate Algebra students students a mean of 7.24 hours with a standard deviation of 1.93 hours. At a level of significance of 5$\%$ , do LTCC Intermediate Algebra students get less than seven hours of sleep per night, on average?
The Type II error is not to reject that the mean number of sleep LTCC students get per night is at lest seven when, in fact, the mean number of hours
a. is more than seven hours.
b. is at most seven hours.
c. is at least seven hours.
d. is less than seven hours.

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Key Concepts

Hypothesis Testing

Hypothesis testing is a statistical method used to make decisions about a population parameter based on sample data. It involves setting up a null hypothesis that represents a baseline or status quo and an alternative hypothesis that reflects the claim being tested. Statistical evidence from sample data is then used to decide whether to reject the null hypothesis in favor of the alternative hypothesis.

Null and Alternative Hypotheses

The null hypothesis (H?) is a default assumption stating that there is no effect or difference, while the alternative hypothesis (H?) is what the researcher aims to support. In one-tailed tests, the alternative hypothesis is directional, specifying whether the parameter is expected to be either less than or greater than a given value.

Type I and Type II Errors

Type I error occurs when a true null hypothesis is incorrectly rejected, indicating a false positive. On the other hand, Type II error happens when the null hypothesis is not rejected even though it is false, representing a false negative. In the context of the question, a Type II error means failing to detect that the true mean differs in the direction indicated by the alternative hypothesis.

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