Question

Literacy rates ~ Tamil Nadu is one of the 29 states in India, which is also one of the leaders in literacy initiatives carried out in India. The literacy rate for Tamil Nadu is 0.799 as per 2011 census data. A NGO wants to determine if the actual literacy rate is different from the value reported in the census data. Recently, the NGO conducted a survey on 1,185 randomly selected Tamil Nadu residents and found that 983 of them are literate. A normal distribution is used to carry out the following hypothesis test: H0:p= 0.799 vs HA:p≠ 0.799. What is the test statistic for this hypothesis test? Give your answer to 4 decimal places.

Answer 1

Answer:

Test statistic = 2.8965

Step-by-step explanation:

The test statistic is given by the formula

z = (x - μ)/σₓ

μ = mean = 0.799

x = proportion of literate people in Tamil Nadu = (983/1185) = 0.8295

σₓ = standard error of this calculated proportion = √[p(1-p)/n]

= √(0.8295 × 0.1705/1185) = 0.01093

z = (x - μ)/σₓ

z = (0.8295 - 0.799)/0.01093 = 2.8965

z = 2.8965

Hope this Helps!!!