Question

You would like to determine if the population probability of success differs from 0.70. You find 62 successes in 80 binomial trials. implement the test at the 1% level of significance. (Y u may find lt useful to reference the appropriate table: z table or t table) a. Select the null and the alternative hypotheses. Hg: P s8.78; HA: P8.78 O He: p 0.78; HA: p < 8.78 b. Calculate the sample proportion. (Round your answer to 3 declmal places.) Sample proportion c. Calculate the value of test statistic. (Round Intermedlate calculatlons to at least 4 declmal places and final answer to 2 declmal places.) Test statistic d. Find the p-value. Op-value<0.01 0.01 s p-value<0.025 0.025 s p-value <o.05 0.05 s p-value 0.10 O p-value 0.10 e. At the 1% significance level, what is the conclusion? OReject He since the p-value is smaller than significance level. O Reject Hg since the p-value is greater than significance level. Do not reject Hg since the p-value is smaller than significance level. Do not reject He since the p-value is greater than significance level.

Answer 1

a)

Ho :   p =    0.7
H1 :   p ╪   0.7
b)

Number of Items of Interest,   x =   62
Sample Size,   n =    80
      
Sample Proportion ,    p̂ = x/n =    0.775

c)

Standard Error ,    SE = √( p(1-p)/n ) =    0.05123
      
Z Test Statistic =    Z = ( p̂-p)/SE =    1.46

d)

p-Value   =   0.1432 (excel formula , =(1-NORMSDIST(1.46))*2

ANSWER(OPTION E )

p-value ≥0.10

e)

Conclusion:     p value>α , don't reject null hypothesis           
option d(answer)

E)