Will the sampling distribution of \( \bar{x} \) always be approximately normally distributed? Explain. Choose the correct answer below. A. Yes, because the Central Limit Theorem states that the sampling distribution of \( \bar{x} \) is always approximately normally distributed. B. No, because the Central Limit Theorem only states that the sampling distribution of \( \bar{x} \) is approximately normally distributed if the sample size is large enough. C. No, because the Central Limit Theorem states that the sampling distribution of \( \bar{x} \) is approximately normally distributed only if the population being sampled is normally distributed. D. No, because the Central Limit Theorem only states that the sampling distribution of \( \bar{x} \) is approximately normally distributed if the sample size is more than \( 5 \% \) of the population.

What does the magnitude of a correlation coefficient indicate about the variables in a correlational study? Multiple Choice strength of the variables relationship between the variables number of data points

Step 4: Determine citical Value Twot aided test \( \bar{w} \) a \( =0.05 \) and \( n-1=15 \) (df Use + distrubution table \( = \pm 2.131 \)

3. Box and Whisker Plot: Draw a box and whisker plot for the data provided and identify any outliers. \( 12,17,13,14,12,16,18,29,15,14,12,17,13,14,12,16,18,29,15,14,12,17,13 \), \[ 14,12,16,18,29,15,14 \]

You wish to test the following claim \( \left(H_{a}\right) \) at a significance level of \( \alpha=0.002 \). \[ \begin{array}{l}H_{a}: \mu_{1}=\mu_{2} \\ H_{a}: \mu_{1}>\mu_{2}\end{array} \] You believe both populations are normally distributed, but you do not know the standard deviations for either. However, you also have no reason to believe the variances of the two populations are not equal. You obtain a sample of size \( n_{1}=20 \) with a mean of \( M_{1}=51.3 \) and a standard deviation of \( S D_{1}=13.2 \) from the first population. You obtain a sample of size \( n_{2}=23 \) with a mean of \( M_{2}=38.8 \) and a standard deviation of \( S D_{2}=8.7 \) from the second population.

2. Scatter Plot and Correlation: Consider the following data points representing the number of hours studied \( (x) \) and the marks obtained \( (y) \) : \[ (1,50),(2,55),(3,60),(4,65),(5,75) \] wa scatter plot and determine whether the relationship between hours studied and marks ositive, negative, or none.