A recent survey of 8,000 high school students found that the mean price of a prom dress was $195.00 with a standard deviation of $12.00. Alyssa thinks that her school is more fashion-conscious and that students spent more than $195.00. She collected data from 20 people in her high school and found that the average price spent on a prom dress was $208.00.

Which of the following are the correct null hypothesis and alternate hypothesis?

A. [tex]H_0: \mu = 195[/tex]; [tex]H_a: \mu > 195[/tex]

B. [tex]H_0: \mu \neq 195[/tex]; [tex]H_a: \mu = 208[/tex]

C. [tex]H_0: \mu = 195[/tex]; [tex]H_a: \mu \neq 195[/tex]

D. [tex]H_0: \mu = 195[/tex]; [tex]H_a: \mu \geq 208[/tex]

Question

High School

Answer :

shubhamchouhanvrVT shubhamchouhanvrVT · Answer 1 · 2023-10-14T02:09:46-04:00

The correct null hypothesis and alternate hypothesis will be

[tex]H_{0} =\mu=195\\H_{a} =\mu > 195[/tex]

It is given that

The mean price of a prom dress was $195. 00 with a standard deviation of $12. 0

Given that Alyssa thinks that her school is more fashion-conscious and that students spent more than $195.00.

She collected data from 20 people in her high school and found that the average price spent on a prom dress was $208.00.

Since she wants to check whether the sample mean [tex]\mu[/tex] is the same as the population mean [tex]\mu[/tex] = 195

[tex]H_{0} =\mu=195\\H_{a} =\mu > 195[/tex]

(Right hypothesis test)

Thus the correct null hypothesis and alternate hypothesis will be

[tex]H_{0} =\mu=195\\H_{a} =\mu > 195[/tex]

To learn more about null hypotheses follow

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