(a) What is the level of significance? State the null and alternate hypotheses. Will do you use a left-tailed, right-tailed, or two-tailed test? (b) What sampling distribution will you use? Explain the rationale for your choice of the sampling distribution. What is the value of the sample test statistic? (c) Find (or estimate) the P-value. Sketch the sampling distribution and show the the area corresponding to the P-value. (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level a? (e) State your conclusion in the context of the application. Let ? be a random variable that represents assembly times for the Ford Taurus. The Wall Street Journal reported that the average assembly time is u = 36 hours. A modification to the assembly procedure has been made. Experience with this new method indicates that o = 1.2 hours. It is thought that the average assembly time may be reduced by this modification. A random sample of 49 new Ford Taurus automobiles coming off the assembly line showed the average assembly time of the new method to be x= 38.5 hours. Doesthis indicate that the average assembly time has been increased? Use a = 0.05.
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.
(a) What is the level of significance? State the null and alternate hypotheses. Will do you use a left-tailed, right-tailed, or two-tailed test?
(b) What sampling distribution will you use? Explain the rationale for your choice of the sampling distribution. What is the value of the sample test statistic?
(c) Find (or estimate) the P-value. Sketch the sampling distribution and show the the area corresponding to the P-value.
(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level a?
(e) State your conclusion in the context of the application.
Let ? be a random variable that represents assembly times for
the Ford Taurus. The Wall Street Journal reported that the average assembly time
is u = 36 hours. A modification to the assembly procedure has been made.
Experience with this new method indicates that o = 1.2 hours. It is thought that
the average assembly time may be reduced by this modification. A random sample
of 49 new Ford Taurus automobiles coming off the assembly line showed the
average assembly time of the new method to be x= 38.5 hours. Doesthis indicate
that the average assembly time has been increased? Use a = 0.05.
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