Question

A survey conducted amongst 180 randomly selected street vendors in Sandton showed that 28 of the vendors felt that local by laws were not ideal for their business. Create a 90% confidence interval for the true proportion ./ of all Sandton vendors who feel that local by–laws are not good for their business. STATS

Answer 1

Solution:

The 90% confidence interval for population proportion is given as follows:

Where, p̂ is sample proportion, q̂ = 1 - p̂, n is sample size and Z(0.10/2) is critical z-value to construct 90% confidence interval.

Sample proportion of street vendors in Sandton who felt that local by laws were not ideal for their business is given by,  p̂ = 28/180 = 0.1556

q̂ = 1 - 0.1556 = 0.8444 and n = 180

Using Z-table we get, Z(0.10/2) = 1.645

Hence, 90% confidence interval for true population proportion of all Sandton vendors who feel that local by–laws are not good for their business is,

The 90% confidence interval for true population proportion of all Sandton vendors who feel that local by laws are not good for their business is (0.1112, 0.2000).

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