Tom Sevits is the owner of the Appliance Patch. Recently, Tom observed a difference in the dollar value of sales between the men and women he employs as sales associates. A sample of 40 days revealed the men sold a mean of $1400 worth of appliances per day. For a sample of 50 days, the women sold a mean of $1500 worth of appliances per day. Assume the population standard deviation for men is $200 and for women $250. At the 0.05 significance level, can Mr. Sevits conclude that the mean amount sold per day is larger for the women? a) State the null hypothesis and the alternative hypothesis. b) What is the decision rule? c) What is the value of the test statistic? d) What is your decision regarding the null hypothesis? e) What is the p-value? f) Interpret the result.
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
Tom Sevits is the owner of the Appliance Patch. Recently, Tom observed a difference in the dollar value of sales between the men and women he employs as sales associates. A sample of 40 days revealed the men sold a mean of $1400 worth of appliances per day. For a sample of 50 days, the women sold a mean of $1500 worth of appliances per day. Assume the population standard deviation for men is $200 and for women $250. At the 0.05 significance level, can Mr. Sevits conclude that the mean amount sold per day is larger for the women?
a) State the null hypothesis and the alternative hypothesis.
b) What is the decision rule?
c) What is the value of the test statistic?
d) What is your decision regarding the null hypothesis?
e) What is the p-value?
f) Interpret the result.
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a) Hypothesis |
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B) |
Population:
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c) |
Null H0 : |
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Alternate HA: |
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D) Decision Criteria |
α = (If Applicable) Left Critical Value: Answer (If Applicable) Right Critical Value: Answer |
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Calculated Value |
Answer Z-Calculated t-Calculated χ2-Calculated F-Calculated ?= Answer |
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Conclusion |
Answer Do NOT Reject null / Reject nullNeither possible |
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P-Value |
P-value= Answer |
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| Conclusion | we conclude there is Answer sufficient orinsufficient evidence to suggest that the mean amount sold per day is larger for the women? |
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