SOLUTION: 50 people were attacked by a disease and 30 were survived. If the survival rate is 70%.Test the claim at 5% level of significance.

Question 1191869: 50 people were attacked by a disease and 30 were survived. If the survival rate is 70%.Test the claim at 5% level of significance.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
30/50 = 60%.
z-score = (x - m) / s
z is the z-score
x is the raw score
m is the mean you are comparing against.
s is the standard error.
s = sqrt(70 * 30)/50) = 6.4807
z = (x - m)/s = (60 - 70) / 6.4807 = -1.54
critical z-score at 5% two sided level of significance is plus or minus 1.96.
-1.96 is more negative than -1.54.
there is not enough evidence to determine that the 70% can be rejected because the results are not significant (not greater than the critical z-score).

if you did this with ratios and not percents, the results would be the same.
s = sqrt(.7*.3/50) = .064807
z = (.6 - .7) / s becomes z = -.1 / .064807 = -1.54.
same z-score.
same result.

here's a reference.
https://online.stat.psu.edu/statprogram/reviews/statistical-concepts/proportions

even if you had done a one tailed test, the critical z-score would have been plus or minus 1.645.
-1.54 is still not greater than -1.645, so the results are still not significant.
this means not enough evidence to overturn the presumed ratio of .7.

RELATED QUESTIONS
20 people were attacked by a disease and only 18 survived .Will you reject the hypothesis (answered by stanbon)

Please help me solve this: A certain brand of alcohol claims that the alcohol... (answered by ewatrrr)

PLEASE HELP ME SOLVE THIS, THANK YOU! A certain brand of alcohol claims that the... (answered by ewatrrr)

A hypothesis has been suggested that a principal benefit of physical activity is to... (answered by proyaop)

Can someone please help me. I have seen other answers but they do not match the ones I... (answered by stanbon)

Multiple myeloma or blood plasma cancer is characterized by increased blood vessel... (answered by jim_thompson5910)

Orbit" bubble-gum company claims that 8 out of 10 people prefer their gum to "Eclipse".... (answered by Boreal)

The lecturer claims that average percentage pass mark of a subject is 60% and the Head of (answered by Boreal)

Directors of a mining company claim that 90% of the workforce supports a new shift... (answered by Boreal)