Final answer:
To test the hypothesis, calculate the sample proportion and compare it to the hypothesized population proportion using a two-sided 95% confidence interval. If the interval includes the hypothesized value, we fail to reject the null hypothesis; if not, we reject it.
Step-by-step explanation:
To test the hypothesis H0: p = 0.9 against H1: p ≠ 0.9 at α = 0.05, we must determine if the sample proportion of satisfied customers significantly differs from the hypothesized population proportion. In the given scenario, a sample of 1000 customers has 850 satisfied or very satisfied, resulting in a sample proportion (p') of 0.85.
For a two-sided 95% confidence interval for the population proportion p, we aim to determine the range of values within which we believe the true proportion lies with 95% certainty. The central limit theorem suggests that for large sample sizes, the sampling distribution of the sample proportion can be approximated by a normal distribution centered around the population proportion (p) with a standard error calculated as √[p(1-p)/n].
If the calculated confidence interval contains the hypothesized proportion (0.9), we fail to reject the null hypothesis. If it does not contain 0.9, we reject the null hypothesis. At the α = 0.05 level of significance, we would expect the critical value to be approximately ±2.576 for constructing a 99% confidence interval.