Test whether the population
Suggest the preferable system.
Answer to Problem 38SE
There is sufficient evidence to conclude that, there is a difference between the population mean checkout times of the two systems.
The preferable system is system A.
Explanation of Solution
Calculation:
The results of the tests on customer checkout times at system A and system B are as follows:
System A | System B |
The level of significance is
State the hypotheses.
The test hypotheses are as follows:
Null hypothesis:
That is, there is no difference between the population mean checkout times of the two systems.
Alternative hypothesis:
That is, there is a difference between the population mean checkout times of the two systems.
Test statistic:
The test statistic for hypothesis tests about
Substitute
Thus, the test statistic is 2.79.
Software procedure:
Step-by-step procedure to obtain the probability value using Excel:
- Open an EXCEL sheet and select the cell A1.
- Enter the formula =NORM.S.DIST(2.79,TRUE) in the cell A1.
- Press Enter.
Output obtained using EXCEL software is given below:
From the output, the p-value for the left tail is 0.997365.
For a two-tailed test, the p-value is two times of upper-tail area.
From the output:
Thus, the p-value is 0.0052.
Rejection rule:
If
If
Conclusion:
Here, the p-value is less than the level of significance.
That is,
From the rejection rule, the null hypothesis is rejected.
Therefore, there is sufficient evidence to conclude that, there is a difference between the population mean checkout times of the two systems.
Thus, there is a difference between the population mean checkout times of the two systems.
Here, the mean checkout time of system B is less when compared to the mean checkout time of system A.
Therefore, system A is preferable.
Want to see more full solutions like this?
Chapter 10 Solutions
Bundle: Modern Business Statistics with Microsoft Office Excel, Loose-Leaf Version, 6th + MindTap Business Statistics, 2 terms (12 months) Printed Access Card
- Let X be a random variable with support SX = {−3, 0.5, 3, −2.5, 3.5}. Part ofits probability mass function (PMF) is given bypX(−3) = 0.15, pX(−2.5) = 0.3, pX(3) = 0.2, pX(3.5) = 0.15.(a) Find pX(0.5).(b) Find the cumulative distribution function (CDF), FX(x), of X.1(c) Sketch the graph of FX(x).arrow_forwardA well-known company predominantly makes flat pack furniture for students. Variability with the automated machinery means the wood components are cut with a standard deviation in length of 0.45 mm. After they are cut the components are measured. If their length is more than 1.2 mm from the required length, the components are rejected. a) Calculate the percentage of components that get rejected. b) In a manufacturing run of 1000 units, how many are expected to be rejected? c) The company wishes to install more accurate equipment in order to reduce the rejection rate by one-half, using the same ±1.2mm rejection criterion. Calculate the maximum acceptable standard deviation of the new process.arrow_forward5. Let X and Y be independent random variables and let the superscripts denote symmetrization (recall Sect. 3.6). Show that (X + Y) X+ys.arrow_forward
- 8. Suppose that the moments of the random variable X are constant, that is, suppose that EX" =c for all n ≥ 1, for some constant c. Find the distribution of X.arrow_forward9. The concentration function of a random variable X is defined as Qx(h) = sup P(x ≤ X ≤x+h), h>0. Show that, if X and Y are independent random variables, then Qx+y (h) min{Qx(h). Qr (h)).arrow_forward10. Prove that, if (t)=1+0(12) as asf->> O is a characteristic function, then p = 1.arrow_forward
- 9. The concentration function of a random variable X is defined as Qx(h) sup P(x ≤x≤x+h), h>0. (b) Is it true that Qx(ah) =aQx (h)?arrow_forward3. Let X1, X2,..., X, be independent, Exp(1)-distributed random variables, and set V₁₁ = max Xk and W₁ = X₁+x+x+ Isk≤narrow_forward7. Consider the function (t)=(1+|t|)e, ER. (a) Prove that is a characteristic function. (b) Prove that the corresponding distribution is absolutely continuous. (c) Prove, departing from itself, that the distribution has finite mean and variance. (d) Prove, without computation, that the mean equals 0. (e) Compute the density.arrow_forward
- 1. Show, by using characteristic, or moment generating functions, that if fx(x) = ½ex, -∞0 < x < ∞, then XY₁ - Y2, where Y₁ and Y2 are independent, exponentially distributed random variables.arrow_forward1. Show, by using characteristic, or moment generating functions, that if 1 fx(x): x) = ½exarrow_forward1990) 02-02 50% mesob berceus +7 What's the probability of getting more than 1 head on 10 flips of a fair coin?arrow_forward
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw HillBig Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin HarcourtCollege Algebra (MindTap Course List)AlgebraISBN:9781305652231Author:R. David Gustafson, Jeff HughesPublisher:Cengage Learning
- Holt Mcdougal Larson Pre-algebra: Student Edition...AlgebraISBN:9780547587776Author:HOLT MCDOUGALPublisher:HOLT MCDOUGAL