Question

the census found an average household size in US is 2.6and sample size 10000
California's average is household size is 2.92 and sample size of 1000 tulare county residents produced an average of 3.38 if we have normal distribution and the population standard deviation is 1.3 is population in California higher than US?
is Tulare County population significantly higher than California?

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 2.6
Alternative Hypothesis, Ha: μ > 2.6

Rejection Region
This is right tailed test, for α = 0.1
Critical value of z is 1.282.
Hence reject H0 if z > 1.282

Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (2.92 - 2.6)/(1.3/sqrt(10000))
z = 24.62

P-value Approach
P-value = 0
As P-value < 0.1, reject the null hypothesis.

2)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 2.6
Alternative Hypothesis, Ha: μ > 2.6

Rejection Region
This is right tailed test, for α = 0.1
Critical value of z is 1.282.
Hence reject H0 if z > 1.282

Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (3.38 - 2.6)/(1.3/sqrt(1000))
z = 18.97

P-value Approach
P-value = 0