Test on a single proportion

A marketing expert for a pasta-making company believes that 40% of pasta lovers prefer lasagna. If 9 out of 20 pasta lovers choose lasagna over other pastas, what can be concluded about the expert’s claim? Use a 0.05 level of significance.

(Textbook Ans : P-value = 0.4044 (with a one-tailed test); the claim is not refuted).

Using binomial distribution to get the P-Value, i have n=10,p=0.40, r=9 and so my answer = 2x 0.7553 (looking up the table) = 1.5106.

(while textbook ans is 0.4044)

so where have i gone wrong ?

Re: Test on a single proportion

My solution emiranda:

Ho: p = 0.4

H1: p > 0.4

Since n = 20, not large enough to use normal approximation for z test statistic.

X: No. of pasta lovers choose lasagna

X ~ Bin (20,0.4)

Since x = 9 > 20(0.4) = 8

P = (X>=9) = 1-(X<9)=1-0.5956(from table) = 0.4044(Cool)

Since P > α=0.05, accept Ho.