Hypothesis Testing?

Question

Can anyone out there do this, because I'm really stuck?

The new cable and TV channel Channel#6 is keen to establish what opinion the viewing public have of its sunday night films. It has undertaken a survey of 100 subscribers and found that 70 like it and 30 don't.

Assuming a constant proportion (in the recent survey) of 70% liking the sunday films, how large a sample is required to detect at 99.5% level that the proportion of subscribers liking the sunday night films has risen from an earlier proportion of 60%?

Answer 1

The test statistic for testing one sample proportion is

z = (phat-p)/sqrt(p(1-p)/n)

Now phat = 0.7 since that value came from your sample. We'll assume that proportion carries through regardless of the sample size.
p = 0.6 since that what you would assume the value is in the null hypothesis.
z = 2.576. Now you said 99.5% level. I'm assuming you mean a 0.5% significance level from that. On the standard normal, 0.5% is found above 2.576

So plug all of those values in and solve for n

2.576 = (0.7-0.6)/sqrt(0.6*0.4/n)
2.576sqrt(0.24/n) = 0.1
sqrt(0.24/n) = 0.1/2.576 = 0.0388
0.24/n = 0.0388^2 = 0.00151
n/0.24 = 1/0.00151 = 663.5776
n = 663.5776*0.24 = 159.258624

Which you should round up every time. You would need a sample size of 160 to make that determination.