Null and alternative hypothesis (1 Viewer)

Hivaclibtibcharkwa · Apr 23, 2022

Can someone help me with these question, like with question b would the null hypothesis be that it’s less than 70 or would the alternative hypothesis say that?

cossine · Apr 23, 2022

Hivaclibtibcharkwa said:
Can someone help me with these question, like with question b would the null hypothesis be that it’s less than 70 or would the alternative hypothesis say that?

The null hypothesis is always an equality. The reason for this is computation.

Because the definition p-value is

p-value = P(getting test statistic that is more contradictory or equally contradictory to the null hypothesis | H0 )

It may help to read Probability and Statistics for Engineering Sciences by Jay L. Devore

It will explain things in more detail

Hivaclibtibcharkwa · Apr 23, 2022

cossine said:
The null hypothesis is always an equality. The reason for this is computation.

Because the definition p-value is

p-value = P(getting test statistic that is more contradictory or equally contradictory to the null hypothesis | H0 )

It may help to read Probability and Statistics for Engineering Sciences by Jay L. Devore

It will explain things in more detail

Ah sorry just realised I didn’t put in the imahe

cossine · Apr 23, 2022

Hivaclibtibcharkwa said:
Ah sorry just realised I didn’t put in the imahe

So give the question a go first and I will check the working out.

In this case

H0: mean_weight = 70
Ha: mean_weight <= 70.

jimmysmith560 · Apr 23, 2022

In general, we reject the null hypothesis if the p-value is less than the significance level α.

If the alternative hypothesis $H_a$ contains the not‐equal‐to symbol (≠), the hypothesis test is a two‐tailed test. Otherwise, all other tests are one-tailed.

If needed, below are solutions to each part, based on the above information. As cossine mentioned, definitely try to attempt the question(s) first to see if you can apply your understanding in your working:

Part (a):

Suppose $\mu$ is the average age of Sydney residents; then $H_0$ is $\mu=35$ , and $H_a$ is $\mu>35$ . Note that this is a one-tailed hypothesis test. Here, the p-value 0.0170 is less than the significance level $\alpha=0.05$ . So we reject the null hypothesis.

Conclusion: this sample information does indicate that the mean age in Sydney has increased from 35 years.

Part (b):

Let $\mu$ be the average weight of this population; then $H_0$ is $\mu=70$ , and $H_a$ is $\mu<70$ . This is a one-tailed test. The standard deviation of weights in this population is $\sqrt{49}=7$ . Here, the p-value 0.001 is less than the significance level $\alpha=0.01$ . So we reject the null hypothesis.

Conclusion: the sample data do provide enough evidence for us to conclude that the mean weight for the population is less than 70 kg.

Part (c):

Let $\mu$ be the average IQ score of this population; then $H_0$ is $\mu=100$ , and $H_a$ is $\mu \ne 100$ . This is a two-tailed test. Here, the p-value 0.095 is greater than the significance level $\alpha=0.05$ . So we do not reject the null hypothesis.

Conclusion: on the basis of these data, we cannot conclude that the mean IQ score for this population is not 100.

I hope this helps!

Hivaclibtibcharkwa · Apr 23, 2022

cossine said:
The null hypothesis is always an equality. The reason for this is computation.

Because the definition p-value is

p-value = P(getting test statistic that is more contradictory or equally contradictory to the null hypothesis | H0 )

It may help to read Probability and Statistics for Engineering Sciences by Jay L. Devore

It will explain things in more detail

Can it also be the greater than or equal to symbol?
3:37 of this video

cossine · Apr 23, 2022

Hivaclibtibcharkwa said:
Can it also be the greater than or equal to symbol?
3:37 of this video

So if you have

H0: mean_weight >= 70
Ha: mean_weight <70

Reject the null hypothesis would be equivalent to rejecting H0: mean_weight=70

For computing the z-value you would have mean_weight=70.

5uckerberg · Dec 22, 2022

Hivaclibtibcharkwa said:
Can someone help me with these question, like with question b would the null hypothesis be that it’s less than 70 or would the alternative hypothesis say that?View attachment 35496

IIRC to determine null and alternative hypothesis the alternative hypothesis is when this statement is true null hypothesis is when it is not.

5uckerberg · Dec 22, 2022

cossine said:
So give the question a go first and I will check the working out.

In this case

H0: mean_weight = 70
Ha: mean_weight <= 70.

I believe for accuracy you should put a tilde above $H_{0}$ because $H_{0}:\mu=70$ is the boundary condition for the question. Like this $\widetilde{H_{0}}:\mu=70$

5uckerberg · Dec 22, 2022

jimmysmith560 said:
In general, we reject the null hypothesis if the p-value is less than the significance level α.

If the alternative hypothesis $H_a$ contains the not‐equal‐to symbol (≠), the hypothesis test is a two‐tailed test. Otherwise, all other tests are one-tailed.

If needed, below are solutions to each part, based on the above information. As cossine mentioned, definitely try to attempt the question(s) first to see if you can apply your understanding in your working:

Part (a):

Suppose $\mu$ is the average age of Sydney residents; then $H_0$ is $\mu=35$ , and $H_a$ is $\mu>35$ . Note that this is a one-tailed hypothesis test. Here, the p-value 0.0170 is less than the significance level $\alpha=0.05$ . So we reject the null hypothesis.

Conclusion: this sample information does indicate that the mean age in Sydney has increased from 35 years.

Part (b):

Let $\mu$ be the average weight of this population; then $H_0$ is $\mu=70$ , and $H_a$ is $\mu<70$ . This is a one-tailed test. The standard deviation of weights in this population is $\sqrt{49}=7$ . Here, the p-value 0.001 is less than the significance level $\alpha=0.01$ . So we reject the null hypothesis.

Conclusion: the sample data do provide enough evidence for us to conclude that the mean weight for the population is less than 70 kg.

Part (c):

Let $\mu$ be the average IQ score of this population; then $H_0$ is $\mu=100$ , and $H_a$ is $\mu \ne 100$ . This is a two-tailed test. Here, the p-value 0.095 is greater than the significance level $\alpha=0.05$ . So we do not reject the null hypothesis.

Conclusion: on the basis of these data, we cannot conclude that the mean IQ score for this population is not 100.

I hope this helps!

Now one-tailed test. That is where you need to know what the alternative hypothesis is pointing at and then you will have the P-value pointing in the same direction towards the test statistic which would be found using a modified z-score technique.

cossine · Dec 22, 2022

5uckerberg said:
I believe for accuracy you should put a tilde above $H_{0}$ because $H_{0}:\mu=70$ is the boundary condition for the question. Like this $\widetilde{H_{0}}:\mu=70$

I have never seen such notation before. Do you have a reference?

5uckerberg · Dec 23, 2022

cossine said:
I have never seen such notation before. Do you have a reference?

Null and alternative hypothesis (1 Viewer)

Hivaclibtibcharkwa

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cossine

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Hivaclibtibcharkwa

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cossine

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