Fry Brothers Heating and Air Conditioning, Inc. employs Larry Clark and George Murnen to make service calls to repair furnaces and air conditioning units in homes. Tom Fry, the owner, would like to know whether there is a difference in the mean number of service calls they make per day. Assume the population standard deviation for Larry Clark is 1.05 calls per day, and 1.23 calls per day for George Murnen. A random sample of 40 days last year showed that Larry Clark made an average of 4.77 calls per day. For a sample of 50 days, George Murnen made an average of 5.02 calls per day. Hypothesis Test: Independent Groups (t test, pooled variance) Larry George 4.77 5.02 mean 1.05 1.23 std. dev. 40 50 n 88 df -0.25000 difference (Larry - George) 1.33102 pooled variance 1.15370 pooled std. dev. 0.24474 standard error of difference 0 hypothesized difference -1.02 t .3098 p-value (two-tailed) -0.73636 confidence interval 95.% lower 0.23636 confidence interval 95.% upper 0.48636 margin of error At the .05 significance level, is there a difference in the mean number of calls per day between the two employees? What is the p-value?
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.
Fry Brothers Heating and Air Conditioning, Inc. employs Larry Clark and George Murnen to make service calls to repair furnaces and air conditioning units in homes. Tom Fry, the owner, would like to know whether there is a difference in the mean number of service calls they make per day. Assume the population standard deviation for Larry Clark is 1.05 calls per day, and 1.23 calls per day for George Murnen. A random sample of 40 days last year showed that Larry Clark made an average of 4.77 calls per day. For a sample of 50 days, George Murnen made an average of 5.02 calls per day.
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Hypothesis Test: Independent Groups (t test, pooled variance) |
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Larry |
George |
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4.77 |
5.02 |
mean |
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1.05 |
1.23 |
std. dev. |
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40 |
50 |
n |
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88 |
df |
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-0.25000 |
difference (Larry - George) |
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1.33102 |
pooled variance |
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1.15370 |
pooled std. dev. |
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0.24474 |
standard error of difference |
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0 |
hypothesized difference |
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-1.02 |
t |
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.3098 |
p-value (two-tailed) |
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-0.73636 |
confidence interval 95.% lower |
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0.23636 |
confidence interval 95.% upper |
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0.48636 |
margin of error |
At the .05 significance level, is there a difference in the mean number of calls per day between the two employees? What is the p-value?
The cutoff score for the .05 significance is between 1.989 and 1.987. Since the t score is -1.02 the we reject the null hypothesis and accept the alternative hypothesis. The p value(probability)
is .3098. This means that about 40% of the time the null hypothesis is going to be true.
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