V Photon is a training device that is designed to improve a user's reaction time. Similar devices have been criticized for being too easy to master, but the makers of Photon say that their device is built to give most users room to improve. The makers say that even among professional athletes, the proportion,p, who can score the top ranking of "light speed" is less than 18%. A random samp|_e of 120 professional athletes is chosen, and 16 score a ranking of "light speed" while using the device. Complete the parts below to perform a hypothesis test to see if there is enough evidence, at the 0.05 level of significance, to support the claim that the proportion of all professional athletes who can score a ranking of "light speedll is less than 18%. (a) State the null hypothesis H0 and the alternative hypothesis H1 that you would use for the test. / Ho: I: P [/3 i H1: I: 2L =D _l X S (b) For your hypothesis test, you will use a Z-test. Find the values of rip and n(1p) to conrm that a Z-test can be used. (One standard is that an 10 and n(1~p)210 under the assumption that the null hypothesis is true.) Here n is the sample size andp is the pmpulation proportion you are testing. np=D X s n(1p)=|:l ts; (c) F n a Z-test and find the p-value. he._ .3 some information to help you with your Z-test. p - p . The value of the test statistic is given by p (1-p) n . The p-value is the area under the curve to the left of the value of the test statistic. Standard Normal Distribution 0.4 Step 1: Select one-tailed or two-tailed. O One-tailed O Two-tailed 0.3 + Step 2: Enter the test statistic. (Round to 3 decimal places.) 0.2+ Step 3: Shade the area represented by the p-value. 0.1 + Step 4: Enter the p-value. (Round to 3 decimal places.)(d) Based on your answer to part (c), choose what can be concluded, at the 0.05 level of significance, about the claim made in the school's reports. 0 Since the value of the test statistic lies in the rejection region, the null hypothesis is rejected. So, there is enough evidence to reject the claim that 38% of students will find a match their first time using the site. 0 Since the value of the test statistic lies in the rejection region, the null hypothesis is not rejected. So, there is not enough evidence to reject the claim that 38% of students will find a match their first time using the site. 0 Since the value of the test statistic doesn't lie in the rejection region, the null hypothesis is rejected. So, there is enough evidence to reject the claim that 38% of students will find a match their first time using the site. 0 Since the value of the test statistic doesn't lie in the rejection region, the null hypothesis is not rejected. So, there is not enough evidence to reject the claim that 38% of students will find a match their first time using the site