Question

A recent article in a college newspaper stated that college students get an average of 6.8 hrs of sleep each night. A student who was skeptical about this value decided to conduct a survey by randomly sampling 29 students. On average, the sampled students slept 5.4 hours per night. Identify which value represents the sample mean and which value represents the claimed population mean.

Answer 1

Answer:

$\bar X=5.4$ represent the sample mean or the statistic calculated from the sample

This value is calculated from the following formula:

$\bar X =\frac{\sum_{i=1}^n X_i}{n}$  

$\sigma$ represent the population standard deviation for the sample  

$n=29$ sample size  

$\mu_o =6.8$ represent the value that we want to test  

Step-by-step explanation:

Data given and notation  

$\bar X=5.4$ represent the sample mean or the statistic calculated from the sample

This value is calculated from the following formula:

$\bar X =\frac{\sum_{i=1}^n X_i}{n}$  

$\sigma$ represent the population standard deviation for the sample  

$n=29$ sample size  

$\mu_o =6.8$ represent the value that we want to test  

$\alpha$ represent the significance level for the hypothesis test.  

z would represent the statistic (variable of interest)  

$p_v$ represent the p value for the test (variable of interest)  

State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the mean is less than 6.8, the system of hypothesis would be:  

Null hypothesis:$\mu \geq 6.8$  

Alternative hypothesis:$\mu < 6.8$