You wish to test the following claim ( \( H_{a} \) ) at a significance level of \( \alpha=0.002 \). \[ \begin{array}{l}H_{o}: \mu=53.1 \\ H_{a}: \mu \neq 53.1\end{array} \] You believe the population is normally distributed, but you do not know the standard deviation. You obtain a sample of size \( n=15 \) with mean \( M=56.5 \) and a standard deviation of \( S D=5.8 \). What is the p-value for this sample? (Report answer accurate to four decimal places.) p-value \( =\square \)

The five-number summary for a data set is: Min \( =14 \quad Q_{1}=40 \quad M=55 \quad Q_{3}=62 \quad \) Max \( =99 \) a Determine the values of the upper and lower fences. b The smallest three values in the data set are \( 6,18,34 \) and the largest are \( 90,94,99 \). Which of these are outliers?

a) Find the critical \( \chi^{2}- \) value for a left-tailed test when \( n=11 \) and \( \alpha=0.01 \). marks] b) Find the critical \( \chi^{2}- \) value for a two-tailed test when \( n=9 \) and \( \alpha=0.05 \). marks]

4 If the point \( (30,50) \) is the point of intersection of the ascending and descending curves, then the sum of its frequency equals \( \begin{array}{llll}\text { (a) } 30 & \text { (b) } 50 & \text { (c) } 60 & \text { (d) } 100\end{array} \)

Four scenarios of statistical studies are given below. Decide which study uses a population parameter. Answer 1000 of the 1883 participants in last year's Ironman in Kona, Hawail were interviewed. \( 68 \% \) of those interviewed said they became interested in triathlons after first ofmpeting in marathons. 351 dog owners who were surveyed, 70 reported owning two dogs. Parkland Hospital performs 15,000 births a year. Of 1000 subjects in a study on multiple births, 38 gave birth to twins. in \( 2001.78 \% \) of children diagnosed with cancer were in remission after five years, and this number is improving.

If a scatter plot shows points that are closely clustered together, what can you infer about the correlation between the variables?