Chapter 5, Problem R5.2RE

(a)

To determine

Discuss the use of random digits table to perform the simulation.

Answer to Problem R5.2RE

Select first two − digits number.

If the number is between 00 and 80 (including both), the toast lands butter side down, otherwise toast lands with butter side up.

Explanation of Solution

Given information:

Probability that the toast lands with butter side down is 0.81.

Such that

  $P\left(\text{toast}\text{lands}\text{with}\text{butter}\text{side}\text{down}\right)=0.81=\frac{81}{100}$

The rows from the random digit table:

  

From random digits table, choose a row.

Select first 2 − digit number.

If the number is between 00 and 80 (including both),

Then

The toast lands with butter side down, else the toast lands with the butter side up.

Repeat until we achieve the results for 10 toasts.

Also,

Keep track of the number of trials that results with butter side down among the 10 toasts.

(b)

To determine

3 trials of simulation using the random digits such that the task performed to be followed by others.

Answer to Problem R5.2RE

First trial: All 10 toasts land butter side down.

Second trial: 9 of the 10 toasts land butter side down and only 1 toast land butter side up

Third trial: 8 of the 10 toasts land butter side down and 2 toasts land butter side up

Explanation of Solution

Given information:

Probability that the toast lands with butter side down is 0.81.

Such that

  $P\left(\text{toast}\text{lands}\text{with}\text{butter}\text{side}\text{down}\right)=0.81=\frac{81}{100}$

The rows from the random digit table:

  

Select first 2 − digit number.

If the number is between 00 and 80 (including both),

Then

The toast lands with butter side down, else the toast lands with the butter side up.

First trial

29: Toast lands butter side down

07: Toast lands butter side down

71: Toast lands butter side down

48: Toast lands butter side down

63: Toast lands butter side down

61: Toast lands butter side down

68: Toast lands butter side down

34: Toast lands butter side down

70: Toast lands butter side down

52: Toast lands butter side down

Note that

All 10 toasts land butter side down.

Second trial

62: Toast lands butter side down

22: Toast lands butter side down

45: Toast lands butter side down

10: Toast lands butter side down

25: Toast lands butter side down

95: Toast lands butter side up

05: Toast lands butter side down

29: Toast lands butter side down

09: Toast lands butter side down

08: Toast lands butter side down

Note that

9 of10 toasts land butter side down and only 1 of 10 toasts land butter side up.

Third trial

73: Toast lands butter side down

59: Toast lands butter side down

27: Toast lands butter side down

51: Toast lands butter side down

86: Toast lands butter side up

87: Toast lands butter side up

13: Toast lands butter side down

69: Toast lands butter side down

57: Toast lands butter side down

61: Toast lands butter side down

Note that

8 of 10 toasts land butter side down and 2 of 10 toasts land butter side up.

(c)

To determine

Whether there is any convincing evidence that the researchers 0.81 probability value is incorrect.

Answer to Problem R5.2RE

There is no convincing evidence exists for researchers 0.81 probability value is incorrect.

Explanation of Solution

Given information:

Probability that the toast lands with butter side down is 0.81.

Such that

  $P\left(\text{toast}\text{lands}\text{with}\text{butter}\text{side}\text{down}\right)=0.81=\frac{81}{100}$

The rows from the random digit table:

  

Dotplot shows the results of 50 simulated trials of dropping 10 pieces of toast:

  

Since

  $0.81\times 10=8.1\approx 8$

It is expected that about 8 of the 10 toasts in the sample to land butter side down.

Moreover,

Note that

8 consists of bulk of dots in the dotplot.

This indicates

It is very likely that 8 of the 10 toasts in the sample land butter side down.

Thus,

There is no convincing evidence that the researchers 0.81 probability value is incorrect.

Also note,

There would be convincing evidence if 8 was unlikely and if all dots would lie on one side of 8 in the dotplot.