Question

One factor in rating a National Hockey League team is the mean weight of its players. A random sample of players from the Detroit Red Wings was obtained. The weight (in pounds) of each player was carefully measured, and the resulting data have a sample size of 17 with a sample mean of 203 pounds and a sample standard deviation of 10.9 pounds. You can assume that all of the assumptions are met. (1 pt.) a) What are the assumptions that are required to perform inference on this data?

Answer 1

Answer:

1) Random: A random sample needs to be obtained in order to apply inference for the mean

2) Normality condition: The sampling distribution of $\bar X$ needs to be approximately normal. If we use a random sample size higher than 30 we can use the Central Limit theorem to verify this condition.

3) Independence: All the individual observations need to be independent. And we need to satisfy that our sample would be lower than 10% of the real population size.

Step-by-step explanation:

For this case we need three conditions:

1) Random: A random sample needs to be obtained in order to apply inference for the mean

2) Normality condition: The sampling distribution of $\bar X$ needs to be approximately normal. If we use a random sample size higher than 30 we can use the Central Limit theorem to verify this condition.

3) Independence: All the individual observations need to be independent. And we need to satisfy that our sample would be lower than 10% of the real population size.

Data given and notation  

$\bar X=203$ represent the sample mean

$s=10.9$ represent the sample standard deviation  

$n=17$ sample size  

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

$\alpha=0.01$ represent the significance level for the hypothesis test.  

t 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 can assume the following system of hypothesis.

Null hypothesis:  $\mu = \mu_o$  

Alternative hypothesis :$\mu\neq \mu_o$  

The degrees of freedom on this case:

$df=n-1=10-1$

Compute the test statistic

The statistic for this case is given by:  

$t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}}$ (1)  

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".