To test the effect of alcohol in increasing the reaction time to respond to a given stimulus, the reaction times of seven people were measured. After consuming 3 ounces of 40% alcohol, the reaction time for each of the seven people was measured again. Do the following data indicate that the mean reaction time after consuming alcohol was greater than the mean reaction time before consuming alcohol? Use = 0.05. (Use before after = d. Round your answers to three decimal places.) Test statistic: t = ? Rejection region: If the test is one-tailed, enter NONE for the unused region. t > ? t < ?PERSON1234567BEFORE5454373AFTER8744366 Solution Formulating the null and alternative hypotheses, Ho: ud <= 0 Ha: ud > 0 At level of significance = 0.05 As we can see, this is a right tailed test. Calculating the standard deviation of the differences (third column): s = 1.505042031 Thus, the standard error of the difference is sD = s/sqrt(n): sD = 0.568852418 Calculating the mean of the differences (third column): XD = -1 As t = [XD - uD]/sD, where uD = the hypothesized difference = 0 , then t = -1.757925198 [ANSWER, TEST STATISTIC] ************************* As df = n - 1 = 6 Then the critical value of t is tcrit = -2.446911851 Hence, Reject Ho when t < -2.4469. [ANSWER] t > NONE. [ANSWER].

1. To understand de Broglie waves and the calculation of wave properties. In 1924, Louis de
Broglie postulated that particles such as electrons and protons might exhibit wavelike properties.
His thinking was guided by the notion that light has both wave and particle characteristics, so he
postulated that particles such as electrons and protons would obey the same wavelength-
momentum relation as that obeyed by light: Lambda = h/p, where Lambda is the wavelength, p
the momentum, and h Planck's constant. Consider a beam of electrons in a vacuum, passing
through a very narrow slit of width 2.00 mu m. The electrons then head toward an array of
detectors a distance 1.013 m away. These detectors indicate a diffraction pattern, with a broad
maximum of electron intensity (i.e., the number of electrons received in a certain area over a
certain period of time) with minima of electron intensity on either side, spaced 0.519 cm from
the center of the pattern. What is the wavelength Lambda of one of the electrons in this beam?
Recall that the location of the first intensity minima in a single slit diffraction pattern for light is
y = Llambda/a, where L is the distance to the screen (detector) and a is the width of the slit. The
derivation of this formula was based entirely upon the wave nature of light, so by de Broglie's
hypothesis it will also apply to the case of electron waves. Express your answer in meters to
three significant figures.
Solution
lambda = h / p
xmin = L lambda / a
lambda = a * xmin / L
= (2 * 10-6 * 0.519 * 10-2) / 1.013
= 1.02 * 10-8 m