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You wish to test the following claim ( \( H_{a} \) ) at a significance level of \( \alpha=0.002 \). \[ \begin{array}{l}H_{0}: \mu_{1}=\mu_{2} \\ H_{a}: \mu_{1}>\mu_{2}\end{array} \] 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.

Find the P-value: Type your answer as a decimial rounded to three decimal places. Do not type a percentage or a percent sign. P.value \( =.055 \) Using an \( \alpha \) level of \( 5 \% \), you should OReject \( H_{0} \) and Accept \( H_{A} \) Accept \( H_{0} \) OFail to Reject \( H_{0} \)

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.

Exam Grades \( A \) statistics professor is used to having a variance in his class grades of no more than 100 . He feels that his current group of students is different, and so he examines a random sample of midterm grades (listed below). At \( \alpha=0.01 \), can it be concluded that the variance in grades exceeds 100 ? Assume the variable is normally distribujed. \( \begin{array}{ccccccc}68.7 & 49.1 & 75.8 & 52.8 & 92.3 & 96.7 & 89.4 \\ 65.2 & 69.5 & 72.8 & 67.5\end{array} \) Send data to Excel.

A local TV station wished to determine if a higher proprotion of women watch the local new They conduct a survey of 200 women and 200 men. Of those surveyed, \( 59 \% \) of women and \( 51 \% \) of men say they watch the local news. Find the P-value: Type your answer as a decimial rounded to three decimal places. Do not type a percentage or a percent sign. P-value=

A local TV station wished to determine if a higher proprotion of women watch the local news. They conduct a survey of 200 women and 200 men. Of those surveyed, \( 59 \% \) of women and \( 51 \% \) of men say they watch the local news.

A local TV station wished to determine if a higher proprotion of women watch the local news. They conduct a survey of 200 women and 200 men. Of those surveyed, \( 59 \% \) of women and \( 51 \% \) of men say they watch the local news.

Suppose that, on average, U.S. adults get fast food 14 times a week. In a random sample of 41 people, it was found that they ordered fast food an average of 15 times in one week. Assume the population standard deviation is 4.3 . Perform a test at a significance level of \( 4 \% \) to determine whether or not the number of times a U.S. adult gets fast food in a week is different from 14.

NO:3 survey was conducted to investigate the association between gender and the likelihood Of articipants in a specific sport. Out of 200 male participants, 120 participated in sport, while out 150 females 60 participated. Calculate the odd-ratio to determine the association between ender and sport also interpret the result.

Durante el 2003 los precios de la gasalina alcanzaron record de precios altos en 16 estados de Estados Unidos (The Wall Street Journal, 7 de marzo de 2003 ). Dos de los estados afectados fueron California y Florida. La American Autamabile Association encontró́ como precio medio muestral por galán \( \$ 2.04 \) en California y \( \$ 1.98 \) por galón en Florida. Use 40 como tamario de la muestra de California y 35 como tamaño de la muestra en Florida. Suponga que estudios anteriores indican que la desviación estándar poblacional en California es 0.10 y en Flarida 0.09 . ¿Existe diferencia entre los precios a un nivel de significancia de 0.01 ?