As the authorized purchasing manager for a large insurance firm, you must decide
ID: 2640706 • Letter: A
Question
As the authorized purchasing manager for a large insurance firm, you must decide if it is good for the company to upgrade office computers. According to your budget the average cost of a desktop computer must be less than or equal to$2,100. using a sample of 64 retailers reveals a mean price of $1,951, with a standard deviation of $242. does the manager proceed with using a 5 percent significant level? As the authorized purchasing manager for a large insurance firm, you must decide if it is good for the company to upgrade office computers. According to your budget the average cost of a desktop computer must be less than or equal to$2,100. using a sample of 64 retailers reveals a mean price of $1,951, with a standard deviation of $242. does the manager proceed with using a 5 percent significant level?Explanation / Answer
Ans. The question is solved as shown below.
Step 1. The given test is a one tailed test and the hypothesis is formulated as below:
Ho : Average cost is less than or equal to $2,100
H1: Average cost is greater than or equal to $2,100
Step 2. Find the value of z statisitic.
Z Statistic = (Mean price- Average cost)/ (Standard Deviation/ ?n)
where n = number of observations
z statistic = ( 1951-2100)/ (242/?64)
= (-149)/ (242/8)
= (-149/30.25) = -4.925619835
Note: As number of observations is greater than 30, we use a Z-test and not t-test.
Step 3. Determine if significance level of 5% i.e 0.05 is significant level for the test
The value of z statistic is -4.925619835. Since the given test is one tailed test and given the alternative hypothesis, the corresponding value of z should be greater than or equal to 1.645, if the desired isgnificance level for the test is 0.05.
Here,as the value of z is --4.925619835 which is neither greater than or equal to 1.645.
Therefore manager does not proceed using a 5% significant level.
Ans: Manager does not proceed using a 5% significant level.
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