Question

The answers are provided in red but I would like to see the calculations and steps about how to get the answers, Thanks:)

08. In an amusement park, a booth costs 2$ to play and rewards participants 10$ if they can shoot within 1cm of some target with a bow and arrow. Before doing his advertisement, the manager wants to make sure that people, on average, shoot at least 2cm away from the target. She randomly selects 9 participants to try the game. Their mean distance from the target was 3cm, with a sample standard deviation of 3cm. a) What would be a sensible null hypothesis (Ho) for the manager to test? Ho: u = 2cm b) Against what alternative hypothesis (Ha) should the manager test the null hypothesis? Hoiu > 2cm c) What is the p-value for this test? 0.2>p-val>.15 d) Should you reject the null at a level of significance of 0.05? Why? No, because the p-value is greater than 0.05. e) If she wants to build a 95% confidence interval with a margin of error of 1cm, at least how many people should she have in her sample? 38 (obtained using t(30), using t(40) also ok)

Answer 1

Given that sample size Sample mean Sample std div X= 3 3=3 To test Ho ll> 20 HUL2 6 Test statistics t = 1 is a X-M. 511 E 3-2 3) va P-value = t=1 V P L tg L 1] 0.8267 ✓ i P-valu = 0.82673 0.05 u d Decision nile is Refect Hoit Puvalue (0.05 fail to I Reject the null hypothesis at 2 0.05 e inn morgin of error for 95% (.I for 1 cm me an

→ tr 12,0-1 x 5/5 2.3060 x 31 vm El n = 47.8587 1 ina les for y ^ 48 ✓ sample size at least 48