Question

Note :

Null hypothesis contain  $=$ , $\leq$ and $\geq$ sign.

and alternative hypothesis contain $\neq$ , $<$ and $>$ sign

If alternative hypothesis contain $\neq$ then test is two tailed test.

If alternative hypothesis contain $<$ then test is left tailed test.

If alternative hypothesis contain $>$ then test is right tailed test.

1) Claimed that the mean IQ of statistics instructors is greater than 120.

Hypothesis - $H_0 : \mu =120$ , $H_a : \mu > 120$ ( claim )    ,   Right tailed test.

2) A dean at JWU claim that the mean time for students to earn a Master's degree in Business is at most 5.2.

Hypothesis - $H_0 : \mu \leq 5.2$ ( claim ) , $H_a : \mu > 5.2$     , Right tailed test

3) A researcher claims that 65% of voters favor gun control..

Hypothesis - $H_a : p = 0.65$ ( claim ) ,   $H_a : p \neq 0.65$ , Two tailed test.

4)

Type I error is the rejection of a true null hypothesis

Type II error is failing to reject a false null hypothesis

Claim : The mean score for all NBA games during a particular season was less than 105 points per game.

Hypothesis : $H_0 : \mu \geq 105$ , $H_a : \mu < 105$ ( claim )

Type I error : Reject null hypothesis $H_0 : \mu \geq 105$ when $\mu \geq 105$ is true.

Type II error : Fail to reject null hypothesis $H_0 : \mu \geq 105$ when $\mu <105$ is true.

5)

Claim is a candidate for governor of RI claims to be favored by at least half of the votes.

Hypothesis -

$H_0 : p \geq 0.5$ ( Claim )

$H_a : p < 0.5$

Let decision is fail to reject null hypothesis .

So conclusion is ,

There is sufficient evidence to support the claim P >= 0.5

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