Question

10. In 2014, 12% of adults said they learned Japanese by watching anime and having the subtitles inEnglish. A recent survey found that 156 of 800 adults said they learned Japanese by watching anime and having the subtitles in English. Test the claim to see if there is a differences from the12% in today’s era at a 0.05 level of significance.(For full credit need to draw the curve and shade the area)

H0:

H1:

Test Stat:

Conclusion:

Answer 1

Solution:
Given in the question
The claim is there is a difference from the12% in today’s era so null and alternate hypothesis can be written as
Null hypothesis H0: p = 0.12
Alternate hypothesis Ha: p 0.12
Number of sample (n)= 800
Number of favourable cases (X)= 156
Sample proportion p^ = X/n = 156/800 = 0.195
Here we will use One proportion Z test as
np = (0.12*800) = 96
n(1-p) = (1-0.12)*800 = 704
As both np and n(1-p) are greater than 5. so test stat value can be calculated as
Test stat = (p^ - p)/sqrt(p*(1-p)/n) = (0.195 - 0.12)/sqrt(0.12*(1-0.12)/800) = 0.075/0.0115 = 6.53
At alpha = 0.05 and this is two tailed test so test critical value = +/-1.96 so if test stat value is less than -1.96 or greater than 1.96 than reject the null hypothesis else do not reject the null hypothesis.
As this test is a two-tailed test, so p-value from the Z table is 0.00001
at alpha = 0.05, we can reject the null hypothesis as p-value is less than alpha (0.00001<0.05). So we can conclude that there is a difference between the12% in today’s era.