Question

Jerry is a district manager for Home Depot and he recently implemented a new safety program in the 8 stores he manages. He would like to know if this new program has resulted in fewer accidents than other Home Depot stores. Jerry knows that the average number of accidents at any Home Depot is 4.2 a month with a standard deviation of 1.1. Jerry’s has the following accident data for his 8 stores. Use a single-sample z-test to determine the outcome (alpha = .05, one-tailed).

Store 1: 2 accidents

Store 2: 1 accidents

Store 3: 4 accidents

Store 4: 3 accidents

Store 5: 5 accidents

Store 6: 1 accidents

Store 7: 0 accidents

Store 8: 2 accidents

provide the following information:

Null Hypothesis in sentence form :

Alternative Hypothesis in sentence form :
Critical Value(s) :

Calculations : Note: the more detail you provide, the more partial credit that I can give you if you make a mistake.

Outcome (determination of significance or not, and what this reflects in everyday language,

Answer 1

Important notations

mean number of accicidents for all the stores.

standard deviation of the number of accicidents for all the stores.

sample mean for the 8 sample stores

s sample standard deviation for the 8 sample stores

n sample size.

level of significance

Now we have the information that

  

So the null hypothesis,

Or the null hypothesis states that there is no effect of his new program. Accident rate remains the same.

The alternative hypothesis

Alternative hypothesis says this new program has resulted in fewer accidents than other Home Depot stores.

the test statistic is

Now i have performed the test in MINITAB software:

Steps required:

1. ENTER the data in a column,name it "number of accidents"
   
2. Stat
3. basic Statistics
4. 1 sample z
5. SELECT as follows   
6. ok
7. ok

So the minitab output is

So,

From minitab output,

the test statitsic z₀=-5.01

the crittcal value is

As,

we reject the null hypothesis .

And accept the alternative hypothesis

So can conclude that the test is significant and,

"this new program has resulted in fewer accidents than other Home Depot stores".

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