Question

The following 5 questions are based on this information. The proportion of headache sufferers who get relief with just two aspirins is 53% (p = 0.53). We plan to take a random sample of 400 headache sufferers. The sampling distribution of is Select one: a. not normal because the sample size is too small O b. not normal because np < 5 O c. normal because np < 5 and n(1 – p) < 5 O d. normal because np > 5 and n(1 - p) > 5

Answer 1

who were Suppose that the proportion of headache sufferers relief with just teve 'aspiring is get P=0.53 (53%), A random sample of 400 headache sufferers fakem. The sampling distribution of Fis. Naincromal because npsrs and noclop)>5 Here npe 400 x0.53 = 212 and n Ci-p)= 40061-0.53)= 188. option d is right answer. The standard error (Sf) of p is given by Þ(1-P) St= SE= 0.53 ×(1-0.53) 0.0 25. 400 b.0.025 answer . option is night answer To find : Poobability that 400 Us headache sufferees will provide sample proportion p) that is a within 0.02 of P.

That is, 0.5l-p 0:55 - Posle 0.51 < 500.55) P-P SECB) seco) PCIP OSI-0.53 0.545-0.53 222 0.025 0.005 P Core - PEo.SC2 < 0.8] P[z c0.8 8]-P[22-018 0.7881 gs. Q119 a. 5.7.62.1. Es the p(0.51 $20.55) = 0.5768 right probability answer To find: that 400 headache sufferers will poovide a Sample proposticó Cp) within 0.09 of p.

Consider P( 6.44 < ] -PC on 044-0.53 C6Q 20.53 cza 0.025 cicas Standardisatio p(-3.6C2C 3,6] = P[203.6] - P[22-3.6] 0.9998- 0.0002 - 0.9996 Or - P(0.44cp 20.62 Option b-0.9996 is the right option. Suppose sample prophton (p) és 0.64. From the above results we can that 99.960% of the time & lies within 0.09 D(populat ton poopootron). > >0.62 is much less likely to occue.Conly 0.0004 chance). option. This is considered str because a Finding ange a sample poopoott otion of 64 1. should be extre be extremely care.
With the given data, we can see that the sample proportion follow Normal distribution.

About 99.96% of the data fall within 0.09 of the population proportion. Thus, sample proportion greater than 0.62 has very little chance of 0.04%.