Question

According to an investment firm, the average 401(k) account balance was $101,000 in 2017. To test if this average has recently changed, suppose a sample of 30 401(k) plans was recently selected, and it was found that the average 401(k) balance was $111,604. Assume that the population standard deviation is $27,154. Using a = 0.01,. State the null and alternative hypothesis.

Answer 1

The null and alternative hypotheses for this scenario can be stated as follows: Null Hypothesis (H0): The average 401(k) account balance is equal to $101,000. Alternative Hypothesis (Ha): The average 401(k) account balance is not equal to $101,000.

Step-by-step explanation:

The null and alternative hypotheses for this scenario can be stated as follows:

Null Hypothesis (H0): The average 401(k) account balance is equal to $101,000.

Alternative Hypothesis (Ha): The average 401(k) account balance is not equal to $101,000.

To test if the average has recently changed, a hypothesis test can be performed. The population standard deviation, sample size, and sample mean are given. Since the population standard deviation is known and the sample size is greater than 30, a z-test can be used. With a significance level of 0.01 (a = 0.01), the critical z-value can be found from the standard normal distribution table, which corresponds to a two-tailed test. The sample mean, population mean, and standard deviation can be used to calculate the test statistic (z-score) using the formula:

z = (sample mean - population mean) / (population standard deviation / sqrt(sample size))

The calculated z-score can then be compared to the critical z-value to determine if the null hypothesis should be rejected or not.