Question

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?

Answer 1

Answer:

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, $\bar{x}$ = $790

Sample size, n = 55

Alpha, α = 0.01

Sample standard deviation, s = $200

First, we design the null and the alternate hypothesis

$H_{0}: \mu = 850\text{ dollars}\\H_A: \mu < 850\text{ dollars}$

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

Formula:

$t_{stat} = \displaystyle\frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}} }$

Putting all the values, we have

$t_{stat} = \displaystyle\frac{790 - 850}{\frac{200}{\sqrt{55}} } = -2.224$

Now, $t_{critical} \text{ at 0.01 level of significance, 54 degree of freedom } = -2.397$

Since,                    

$t_{stat} > t_{critical}$

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.