Question

In a sample of 150 households in a certain city, 110 had high-speed internet access. Can you conclude that more than 70% of the households in this city have high speed internet access?

Answer 1

Answer:

Yes, we can conclude that more than 70% of the households in this city have high speed internet access

Step-by-step explanation:

given that in a sample of 150 households in a certain city, 110 had high-speed internet access.

Sample proportion = $\frac{110}{150} \\=0.7333$

Hypothetical proportion is 0.70

Hence std error of p = $\sqrt{\frac{pq}{n} } \\=\sqrt{\frac{0.7*0.3}{150} } \\=0.03742$

$H_0: p = 0.7\\H_a: p \neq 0.7$

(two tailed test at 5% level)

p difference = 0.0333

Test statistic Z = p diff/std error = 0.891

p value = 0.379

since p value is >0.05, we accept H0

Yes, we can conclude that more than 70% of the households in this city have high speed internet access