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Suppose a recent plant journal indicated that the mean height of mature plants of a certain species of sunflower is 10.1 ft. A biologist observing a huge field of mature plants of this particular species of sunflower thinks that the mean height is shorter than reported. He measures the heights of 35 randomly selected sunflowers and finds the mean height to be 9.6 ft. Select the correct null, H 0 , and alternative, H 1 , hypotheses.

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Answer:

Null hypothesis:[tex]\mu \geq 10.1[/tex]  

Alternative hypothesis:[tex]\mu < 10.1[/tex]  

Or equivalently :

Null hypothesis:[tex]\mu = 10.1[/tex]  

Alternative hypothesis:[tex]\mu < 10.1[/tex]  

Step-by-step explanation:

Data given and notation  

[tex]\bar X=9.6[/tex] represent the sample mean

[tex]s[/tex] represent the sample standard deviation for the sample  

[tex]n=35[/tex] sample size  

[tex]\mu_o =10.1[/tex] represent the value that we want to test

[tex]\alpha=[/tex] represent the significance level for the hypothesis test.  

t would represent the statistic (variable of interest)  

[tex]p_v[/tex] represent the p value for the test (variable of interest)  

State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the true mean is lower than 10.1 ft (alternative hypothesis) , then the system of hypothesis would be:  

Null hypothesis:[tex]\mu \geq 10.1[/tex]  

Alternative hypothesis:[tex]\mu < 10.1[/tex]  

Or equivalently :

Null hypothesis:[tex]\mu = 10.1[/tex]  

Alternative hypothesis:[tex]\mu < 10.1[/tex]  

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