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## CSU The Null and Alternative Hypotheses for a Decision Essay

### Question Description

Example 1:

We allknow the importance of saving money for retirement. In order to livecomfortably in old age, we must make smart fiscal decisions while we arestill relatively young in order to prepare ourselves for life afteremployment. A widely used retirement savings account, the 401k, limitsthe amount of contribution that any holder may put in each month to\$19,500 (Unless you are over 50 in which case you may contribute\$26,000). I would like to test the hypothesis that people, on average,max out their contributions each month.

Ho = People under 50, on average, put the maximum contribution of \$19,500 into their 401Ks each month.

Ho: ? = \$19,500

HA = People under 50, on average, put the less than the maximum contribution of \$19,500 into their 401Ks each month.

HA = ? < \$19,500

I will use the normal distribution for the test statistic:

${z}_{c}=\frac{\left(x?{?}_{0}\right)}{\left(\frac{s}{\sqrt{n}}\right)}$

(Holmes et al., 2017).

The alternative hypothesis is left-tailed because it is testingwhether or not people put less money into their 401ks than the maximumamount assumed by the null hypothesis.

I would use the standard 95% significance in this experiment becauseit allows for a small amount of data to be outliers but not so little asa 99% significance which seems extreme.

Type 1 error: If I mistakenly reject the null hypothesis (Holmes et al., 2017). (That the average contribution is \$19,500)

Type 2 error: If I mistakenly fail to reject the null hypothesis(Holmes et al., 2017). (That the average contribution is \$19,500)

References:

Holmes, A., Dean, S., Hadley, K., & Illowsky, B. (2017). Introductory Business Statistics. Huston, TX : OpenSource.

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