Question

After listening to his physical education professor's lecture about healthy eating habits, Alex decides to investigate how many Calories his classmates eat on an average day. Alex's professor claims that the number of Calories eaten for any given student is normally distributed with mean μ and standard deviation σ. Suppose Alex decides to randomly select n students from his school and ask each student how many Calories he or she eats on a typical day. The sampling distribution of Alex's one-sample t-statistic follows a a. t-distribution with n degrees of freedom. b. i-distribution with mean (u and standard deviation c. normal distribution with mean 0 and standard deviation 1. d. t-distribution with n 1 degrees of freedom. e. normal distribution with mean fi and standard deviation ơ.

Answer 1

The sampling distribution of Alex's one-sample t-statistic follows a a. t-distribution with n degrees of freedom.

Step-by-step explanation:

The t-distribution, also known as Student's t-distribution, is a probability distribution used in statistics. It is commonly employed for hypothesis testing and constructing confidence intervals for population means when the sample size is small or the population standard deviation is unknown.

The sampling distribution of Alex's one-sample t-statistic follows a t-distribution with n degrees of freedom. In this case, since Alex randomly selects n students from his school and asks each student about the number of Calories they eat on a typical day, the t-distribution is the appropriate distribution to use. The degrees of freedom for the t-distribution is equal to the number of students surveyed (n) minus 1. This means that the sampling distribution of Alex's one-sample t-statistic will have a t-distribution with (n-1) degrees of freedom.

Answer 2

The sampling distribution of Alex's one-sample t-statistic follows a t-distribution with n degrees of freedom.

Step-by-step explanation:

The sampling distribution of Alex's one-sample t-statistic follows a t-distribution with n degrees of freedom. This means that when Alex randomly selects n students and asks each student how many Calories they eat on a typical day, the distribution of the t-statistic will follow the t-distribution. The degrees of freedom for this t-distribution is equal to n-1, where n is the number of students sampled.