Data from the Office for National Statistics show that the mean age at which men in Great Britain get married was 32.5 . A news reporter noted that this represents a continuation of the trend of waiting until a later age to wed. A new sample of 47 recently wed British men provided their age at the time of marriage. This data is contained below. Age- \( 26,36,27,30,28,26,36,33,25,30,31,34,26,33,29,32,30,39 \), \( 34,27,30,30,35,26,28,29,36,28,28,26,38,25,35,40,26,35,35,27 \), \( 33,29,28,33,38,39,35 \) Do these data indicate that the mean age of British men at the time of marriage exceeds the mean age in 2013 ? Test this hypothesis at a= 0.01. What is your conclusion? Use the obtained rounded values in your calculations. Sample mean: Sample standard deviation: t-value: p-value (Upper Tail):

(b) Consider the hypotheses \( \mathrm{H}_{0}: \mu=101 \) versus \( \mathrm{H}_{1}: \mu>101 \). Explain what the director is testing. Perform the test at the \( \alpha=0.01 \) level of significance. Write a conclusion for the test Explain what the director is testing. Choose the correct answer below. A. The director is testing if the sample provided sufficient evidence that the population mean IQ score is actually not equal to 101 . C. The director is testing if the sample provided sufficient evidence that the population mean IQ score is actually equal to 101 . D. The director is testing if the sample provided sufficient evidence that the population mean IQ score is actually not greater than 101 . Find the test statistic for this hypothesis test. 1.26 (Round to two decimal places as needed.) Find the P -value for this hypothesis test. (Round to three decimal places as needed.)

If the number 31 is added to the data set \( 3,5,6,6,8,11,12,22,26 \), by what value will the average of the data set increase?

If the number 31 is added to the data set \( 3,5,6,6,8,11,12,22,26 \), by what value will the average of the data set increase?

(c) Consider the hypotheses \( \mathrm{H}_{0}: \mu=104 \) versus \( \mathrm{H}_{1}: \mu>104 \). Explain what the director is testing. Perform the test at the \( \alpha=0.01 \) level of significance. Write a Explain what the director is testing. Choose the correct answer below. A. The director is testing if the sample provided sufficient evidence that the population mean lQ score is actually not greater than 104 . The director is testing if the sample provided sufficient evidence that the population mean lQ score is actually greater than 104. C. The director is testing if the sample provided sufficient evidence that the population mean IQ score is actually not equal to 104 . D. The director is testing if the sample provided sufficient evidence that the population mean IQ score is actually equal to 104. Find the test statistic for this hypothesis test. 0.83 (Round to two decimal places as needed.) Find the P-value for this hypothesis test. \( \square \) (Round to three decimal places as needed.)

I. Se refieren a indicadores de posición que dividen en cuatro partes porcentuales iguales una distribución de datos ordenados. II. El segundo cuartil corresponde a la mediana de la distribución de datos. III. El tercer cuartil indica el valor mínimo que toma el \( 75 \% \) de la distribución ordena de datos. IV. El cuartil uno es equivalente al decil 2 . De las anteriores afirmaciones cuál o cuáles son verdaderas: Seleccione una: I y IV II I y II II y III.