Question

One measure of a country’s wealth is the average saving account balance among households. Suppose in 2016 the average saving account balance among households of a country was reported to be $29700. The same survey was performed in 2019 with a random sample of 850 households, and the average balance was found to be $30500. The distribution of saving account balance is right-skewed due to households with high incomes. Assume the standard deviation of this distribution to be $14500. Carry out a significance test at the 0.05 significance level to determine whether the average saving account balance among households in this country has increased since 2016. Be sure to perform all the steps including the hypothesis and a conclusion without any technical terms.

Answer 1

• Given that,
  population mean(u)=29700
  sample mean, x =30500
  standard deviation, s =14500
  number (n)=850

• 
  null, Ho: μ=29700
  alternate, H1: μ > 29700

• 
  level of significance, α = 0.05
  from standard normal table, two tailed Z α =1.64
  since our test is one-tailed
  reject Ho, if Zo > 1.64

• 
  we use test statistic (z) = x-u/(s.d/sqrt(n))
  zo =29700-30500/(14500/sqrt(850))
  zo =1.6085
  critical value the value of Zα is 1.64
  we got zo =1.6085 & zα =1.64
  make decision
  hence value of z0 <zα and here we fail to3 reject Ho

• 
  p-value : one tailed p(Z> 1.6085) = 0.0538
  Since pvalue > 0.05,here we fail to reject Ho

we have not enough evidence to support the claim that the average saving account balance among households in this country has increased since 2016.