It is believed that Lake Tahoe Community College (LTCC) Intermediate Algebra students get less than seven hours of sleep per night, on average. A survey of $22$ LTCC Intermediate Algebra students generated 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 distribution to be used for this test is $\overline{X}~$________________

a. $N(7.24$, $\frac{1.93}{\sqrt{22}}$)

b.$N(7.24,1.93)$

c. $t_{22}$

d. $t_{21}$

Perform tests of a population mean using a normal distribution or a Student's t-distribution.

Here we have the population mean and population standard deviation and so we may do a normal distribution test. When testing a single population proportion use a normal test for a single population proportion if the data comes from a simple, random sample, fill the requirements for a binomial distribution, and the mean number of successes and the mean number of failures satisfy the conditions: $np>5$ and $nq>5$ where n is the sample size, $p$ is the probability of success, and $q$ is the probability of a failure.

The correct option is a.

Since we have the values of mean and standard deviation we go for a.

When you perform a hypothesis test of a single population mean μ using a normal distribution (often called a z-test), you take a simple random sample from the population.