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ASSIGNMENT 4 SSE5091 (INDIVIDUAL)

PARAMETRIC TEST

(DUE ON: 10/1/2024)

1. A new 8-bit microcomputer chip has been developed that can be reprogrammed without removal from the microcomputer. It is claimed that a byte of memory can be programmed in less than 14 seconds.

a) Set up the appropriate null and alternative hypotheses needed to verify this claim.

b) What is the critical value for an =.05 level test based on a sample of size 15?

c) These data are obtained on X, the time required to reprogram a byte of memory

Test the null hypothesis. Can H0 be rejected at the =0.05 level? Conclude your result based on the critical value in part b).

d) Approximate the p-value for test statistic.

e) What happened when =0.01 is used? Will the conclusion be the same?

a) Null hypothesis (H_0): The average time to program a byte of memory is 14 seconds or more.

Alternative hypothesis (H_1): The average time to program a byte of memory is less than 14 seconds.

b)  n=15   df =n-1=14

2. Independent random samples were selected from populations 1 and 2. The sample sizes, means, and variances are as follows

a) Suppose you wish to detect a difference between the population means. State the null and alternative hypothesis for the test

b) Check the appropriate use of common variance between the two populations then calculate the common variance, s2 of the population variance.

c) Find the value of the test statistic to detect a difference between the population means. Use =.05 to reject your null hypothesis.

3. We did a survey of 7 students who had passed Programming II and then we have asked for their grades in Programming I and Programming II. This is the data:

Note: Assume that Programming II is population 1 and Programming I is population 2

We want to test whether there is improvement in the students’ grades from Programming I to Programming II.

a) Which test would you perform in this case?

b) What is the critical value at the 5% significance level?

c) Conduct the test statistic and conclude your result based on the critical value in part b).

d) Approximate the p-value for test statistic.

4. A study is conducted to compare the variability in the number of hours that a rechargeable flashlight will operate after its battery has been fully charged. These data are obtained for two different brands of batteries:

Use these data to test for equality of variances. Can you conclude that the variances are unequal at the =.05 level?

ANOVA

5. The compiling time (seconds) for four different programs has been measured. The result is:

Program 1: 5.7, 6.3, 6.1, 6.0, 5.8, 6.2

Program 2: 6.2, 5.3, 5.7, 6.0, 5.2, 5.5

Program 3: 5.4, 5.0, 6.0, 5.6, 4.9, 5.2

Program 4: 3.7, 3.2, 3.9, 4.0, 3.5, 3.6

a) Calculate CM and Total SS.

b) Calculate SST and Total MST.

c) Calculate SSE and Total MSE.

d) Construct ANOVA table for the data.

e) State the null and alternative hypotheses for an analysis of variance of F-test.

f) Use the p-value approach to determine whether there is a difference in the four programs means.

a)  CM=G²/n=124²/24=646.67

  Total SS=22.03

b)  

6. Three treatments were randomly selected from a large population of possible treatments. Ten randomly selected observations were then obtained from each treatment selected.

a) State an appropriate null hypothesis to be tested, and list all assumptions necessary to make this test for the described experiment.

b) The data yielded the following partial analysis of variance table:

Complete the ANOVA table, and test your null hypothesis in part (a) at the 0.05 level of significance

7. A randomized block design was used to compare the means of five treatments within seven blocks.

a) Construct an ANOVA table showing the sources of variation and their respective degrees of freedom.

b) Suppose that the analysis of variance calculations are SST = 14.2, SSB = 18.9, and Total SS = 41.9. Complete the ANOVA table, showing all sums of squares, mean squares and pertinent F-values. Do the data provide sufficient evidence to indicate differences among the treatment means? Test the hypothesis using =.05.

c) Do the data provide sufficient evidence to indicate differences among the blocking means? Justify your answer.

CHAPTER 9

8. Consider a study of relationship between the CPU time and the number of I/0s usage is conducted; a sample of data on service calls was taken. The data consist of the CPU time in minutes (the response variable, y) and the number of units repaired (the predictor variable, x). The data are presented as:

a) Draw the corresponding scatter plot of Y versus X. Does the assumption of a linear relationship appear to be reasonable?

b) Find the least-squares line relating the CPU time (y) to number of I/Os (x).  

c) Construct the ANOVA table for the linear regression.

d) Is the number of I/Os usage useful in predicting the CPU time? Use the appropriate statistical test and measures to explain the usefulness of the regression model.

9. Table below shows data relating x, the number of books written by Professor Isaac to y, the number of months he took to write his books (in increments of 100).

a) Construct the ANOVA table for the linear regression.

b) Do the data support the hypothesis that β=0? Use the p-value approach to conclude your result.