The mean balance of all checking accounts at a bank on december 31, 2011, was $850. a random sample of 55 checking accounts taken recently from this bank gave a mean balance of $790 with a standard deviation of $200. using the 1% significance level, can you conclude that the mean balance of such accounts has decreased during this period?

There is insufficient evidence to conclude that the mean balance of accounts has decreased during this period

Step-by-step explanation:

We are given the following in the question:  

Population mean, μ = $850

Sample mean, = $790

Sample size, n = 55

Alpha, α = 0.01

Sample standard deviation, s = $200

First, we design the null and the alternate hypothesis

We use one-tailed t test to perform this hypothesis.

Formula:

Putting all the values, we have

Now,

Since,                    

We fail to reject the null hypothesis and accept the null hypothesis.  There is insufficient evidence to conclude that the mean balance of accounts has decreased during this period.