PLZ HELP ME I WAS STUCK ON THIS FOR 30 MINS WILL GIVE BRAINLIST
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Answer:
We conclude that the second graders who participate in sports does not have a higher mean dexterity score.
Step-by-step explanation:
We are given that a random sample of 37 second graders who participated in sports had manual dexterity scores with mean 32.19 and standard deviation 4.34. An independent sample of 37 second graders who did not participate in sports had manual dexterity scores with mean 31.68 and standard deviation 4.56.
We have to conduct a hypothesis test to see whether sufficient evidence exists to indicate that second graders who participate in sports have a higher mean dexterity score.
<em>Let </em><em> = population mean dexterity scores for second graders who participated in sports</em>
<em> </em><em> = population mean dexterity scores for second graders who did not participated in sports</em>
SO, Null Hypothesis, :
or
{means that the second graders who participate in sports have less than or equal mean dexterity score}
Alternate Hypothesis, :
or
{means that the second graders who participate in sports have a higher mean dexterity score}
The test statistics that will be used here is <u>Two-sample t test statistics</u> as we don't know about the population standard deviations;
T.S. = ~
where, = sample mean dexterity scores for 37 second graders who participated in sports = 32.19
= sample mean dexterity scores for 37 second graders who did not participated in sports = 31.68
= standard deviation for 37 second graders who participated in sports = 4.34
= standard deviation for 37 second graders who did not participated in sports = 4.56
= sample size for second graders who participated in sports = 37
= sample size for second graders who did not participated in sports = 37
Here, =
= 4.45
So, <u>test statistics</u> = ~
= 0.493
<em> So, at 0.05 level of significance, the t table gives critical value of 1.6684 at 72 degree of freedom for one-tailed test. Since our test statistics is less than the critical value of t so we have insufficient evidence to reject null hypothesis as it will not fall in the rejection region.</em>
Therefore, we conclude that the second graders who participate in sports does not have a higher mean dexterity score.
Check the picture below.
now, let's notice the larger "yellow" semicircle, it has a gap, the gap on the right is of a semicircle with a diameter of 10, BUT it also has a descender on the left, a part that's hanging out, that part is also a semicircle.
so if we use the descending semicircle to fill up the gap on the right, we'll end up with a filled up larger semicircle, whose diameter is 20, and whose radius is 10 cm.
