Null Hypothesis/Alternative hypothesis, statistics help

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In summary, the null and alternative hypotheses for each question are stated using symbols: For question a, the null hypothesis is that the average speed is equal to or less than 65, while the alternative hypothesis is that the average speed is greater than 65. For question b, the null hypothesis is that the mean height is equal to 50, while the alternative hypothesis is that the mean height is not equal to 50. For question c, the null hypothesis is that the mean IQ is equal to or higher than 100, while the alternative hypothesis is that the mean IQ is lower than 100. For question d, the null hypothesis is that the average daily high temperature is equal to or less than 30, while the alternative hypothesis
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Null Hypothesis/Alternative hypothesis, statistics help!

Homework Statement


For each of the following questions, state(using symbols) the null and alternative hypotheses.
a.)Does the average speed of vehicles on the Thruway exceed 65?
b.) Is the mean height of 6th graders different from 50 inches?
c.) Is the mean IQ of a sample of 60 children significantly below the national average of 100?
d.) In January, does the average daily high temperature exceed 30 degrees?
e.) Is the proportion of males enrolled at the college more than that expected by chance?


Homework Equations


(work shown below)


The Attempt at a Solution


a.) Average speed >/= 65
Average speed </= 65
b.) The mean height of 6th graders is not different from 50 inches.
The mean height of 6th graders is different from 50 inches.
c.) The mean IQ of a sample of 60 children is not significantly below the national average of 100.
The mean IQ of a sample of 60 children is significantly below the national average of 100.
d.) In January, the average daily high temperature does not exceed 30 degrees.
In January, the average daily high temperature does exceed 30 degrees.
e.) The proportion of males enrolled at the college is not more than that expected by chance.
The proportion of males enrolled at the college is more than that expected by chance.

(I NEED HELP ALSO KNOWING WHETHER TO USE Ho : p or Ho:(micro symbol)
 
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as my null hypothesis)

a.) Ho: µ ≤ 65
Ha: µ > 65

b.) Ho: µ = 50
Ha: µ ≠ 50

c.) Ho: µ ≥ 100
Ha: µ < 100

d.) Ho: µ ≤ 30
Ha: µ > 30

e.) Ho: p ≤ 0.5
Ha: p > 0.5
 

What is the difference between a null hypothesis and an alternative hypothesis?

A null hypothesis is a statement that assumes there is no significant difference between two or more variables. It is the default position that is tested against the alternative hypothesis, which is a statement that assumes there is a significant difference between two or more variables. The alternative hypothesis is typically the hypothesis that the researcher is trying to prove.

How do you determine if a null hypothesis is rejected or not?

In order to determine if a null hypothesis is rejected, the researcher will conduct a statistical test using the data collected from their study. The results of the test will either support or reject the null hypothesis. If the results are statistically significant, meaning that the probability of obtaining the results by chance is very low, then the null hypothesis is rejected in favor of the alternative hypothesis.

What is the p-value and how is it related to the null hypothesis?

The p-value is the probability of obtaining a result that is at least as extreme as the one observed in the data, assuming that the null hypothesis is true. In other words, it is the likelihood of obtaining the observed results by chance alone. A small p-value (usually less than 0.05) indicates that the null hypothesis is unlikely to be true and should therefore be rejected in favor of the alternative hypothesis.

What is a Type I error and a Type II error in hypothesis testing?

A Type I error, also known as a false positive, occurs when the null hypothesis is rejected even though it is actually true. This means that the researcher concludes that there is a significant difference between variables when there is not. A Type II error, also known as a false negative, occurs when the null hypothesis is not rejected even though it is actually false. This means that the researcher fails to detect a significant difference between variables when there is one.

What are some common misconceptions about null and alternative hypotheses?

One common misconception is that the null hypothesis is always the opposite of the alternative hypothesis. This is not always the case, as the null hypothesis can also assume no difference or no relationship between variables. Another misconception is that a statistically non-significant result means that the null hypothesis is true. This is not necessarily true, as a non-significant result could also be due to a lack of power in the study. Additionally, rejecting the null hypothesis does not necessarily mean that the alternative hypothesis is true, it only means that the null hypothesis is highly unlikely to be true based on the data.

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