Question

Data from a 2006 GSS subsample show that the mean number of children per respondent was 1.87, with a standard deviation of 1.64. A total of 1,494 people answered this question. Estimate the population mean number of children per adult using a 90% confidence interval. We our 90% confident that the population mean number of children per adult is between to . Please round to the nearest tenth For example, rounding 0.843 to the nearest tenth would give 0.8.

Answer 1

We are 90% confident that the population mean number of children per adult is between 1.8 to 1.9.

Explanation:

The confidence interval for population mean is given by:-

`\overline{x}\pm z^*(\sigma)/(√(n))`, where n= sample size,
`\overline{x}` = sample mean, z* = critical value for confidence level,
`\sigma`= standard deviation.

z* for 90% confidence level = 1.645

As per given, the required confidence interval is

`1.87\pm (1.645)(1.64)/(√(1494))\\\\\approx1.87\pm0.070\\\\=(1.87-0.07,\ 1.87+0.07)\\\\=(1.8, 1.94)`

Hence, We are 90% confident that the population mean number of children per adult is between 1.8 to 1.9.