Answered: Listed below are actual high…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Actual high temperature	73	78	76	73	79	73	81	76
High temperature forecast one day before	71	76	76	73	77	76	83	79

Part 2

What is the test statistic?

T=enter your response here

(Type an integer or a decimal.)

Part 3

Identify the critical value.

The critical value is

enter your response here.

Part 4

What is the conclusion?

There

▼

is not

enough evidence to warrant rejection of the claim that the population of differences

▼

does not have

has

a median of zero. Based on the sample data, it appears that the predictions

▼

are not

are

reasonably accurate

Below is a transcription of the educational content, including details about any included graphs or diagrams.

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**Listed below are actual high temperatures and the high temperatures forecast one day in advance. Use a 0.10 significance level to test the claim that the population of differences has a median of zero. What do the results suggest about the accuracy of the predictions?**

- **Actual high temperatures:** 73, 78, 76, 79, 79, 81, 76
- **High temperature forecast one day before:** 71, 76, 73, 76, 77, 83, 79

**What are the hypotheses for this test?**

- $ H_0 $: The median of the differences is **equal to** zero.
- $ H_1 $: The median of the differences is **not equal to** zero.

**What is the test statistic?**

- $ T = $ [Type an integer or a decimal.]

**Identify the critical value.**

- The critical value is [ ]

**What is the conclusion?**

- There is [ ] enough evidence to warrant rejection of the claim that the population of differences has a median of zero. Based on the sample data, it appears that the predictions [ ] reasonably accurate.

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**Data table**

This table provides critical values of $ T $ for the Wilcoxon Signed-Ranks Test. It includes critical values for different significance levels (α) and tail types.

- The columns specify significance levels for one tail (0.005, 0.01, 0.025, 0.05, 0.10) and two tails (0.01, 0.02, 0.05, 0.10).

- The leftmost column lists the sample size (n).

For example:
- For a sample size of 10 with a one-tail significance level of 0.05, the critical value is 8.

(Note: Cells with '*' indicate it's not possible to get a value in the critical region.)

Definition Definition Middle value of a data set. The median divides a data set into two halves, and it also called the 50th percentile. The median is much less affected by outliers and skewed data than the mean. If the number of elements in a dataset is odd, then the middlemost element of the data arranged in ascending or descending order is the median. If the number of elements in the dataset is even, the average of the two central elements of the arranged data is the median of the set. For example, if a dataset has five items—12, 13, 21, 27, 31—the median is the third item in ascending order, or 21. If a dataset has six items—12, 13, 21, 27, 31, 33—the median is the average of the third (21) and fourth (27) items. It is calculated as follows: (21 + 27) / 2 = 24.

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