(d) Given that \( \widehat{\beta}_{1}=0.72 \) and that the sample variances of \( X \) and \( Y \) are 0.3 and 0.25 , respectively, what is the linear correlation coefficient of \( X \) and \( Y \) ? Show your workings.

SlackBoard, a company producing a Learning Management System (LMS), knows that their average user has historically spent about 75 minutes per day logged into their SlackBoard classes. They also know that time spent logged in is approximately normally distributed. A recent random sample of 58 accounts resulted in an average time of 92 logged in per day with a standard deviation of 69 minutes per day. Formulate and test a hypothesis to determine whether there is evidence to that there has been a change in average individual use time per day. Conduct your test at a significance level of \( \alpha=0.01 \). Your hypotheses are: \( \begin{array}{l}H_{0}: \mu=75 \\ H_{0}: \mu>75 \\ H_{a}: \mu>0 \\ H_{0}: \mu=75 \\ H_{a}: \mu<75 \\ H_{0}: \mu=75 \\ H_{a}: \mu \neq 75 \\ \sigma\end{array} \) What is the test statistic for this test? test statistic \( =\square \) What is the p -value for this test? p-value \( =\square \) (Report answer accurate to 4 decimal places.)

A restaurant owner is interested in the proportion of his customers who order dessert. He looks at 65 randomly selected receipts. Match the vocabulary word with its corresponding example. - The 65 restaurant patrons whose receipts were observed by the owner - The proportion of the 65 randomly selected customers who ordered dessert answer: Yes or No to whether a customer ordered dessert a. Parameter who come to the restaurant of the 65 Yes or No answers for whether each customer ordered dessert. b. Variable c. Sample d. Population e. Data f. Statistic

2.- Si las estaturas de un conjunto de personas adultas se distribuyen aproximadamente contorme a una curva normal y si su promedio aritmético y desviación estándar son respectivamente; 1.62 y 0.03 metros. Encuentre: (valor \( 10 \% \) ) A) La probabilidad de que un cierto número de personas tengan una estatura entre 1.64 y 1.67 . B) La probabilidad de que un cierto número de personas tengan una estatura entre la media y \( x=1.66 \).

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

4. Un estudio lievado a cabo en cierto distrito escolar dio como resultado que el \( 70 \% \) de los niños de primaria habian mudado de casa por lo menos una ver en su vida. Se saca una muestra aleatoria de 200 niños de este distrito. ¿Cual es la probabilidad de que la proporción de los nif̄os que han mudado de casa por lo menos una vez en su vida esté entre: 0.65 y 0.75 ? y cual es la probabilidad de que la proporción sea mayor que 0.75 ?