Statistics Home Work I need help on?

Question

The student body at St. Algebra college attends an average of 3.3 parties per month. A random sample of 117 sociology majors average 3.8 parties per month with a standard deviation of 0.53. Ar sociology majors significantly different formt the student body as a whole? (HINT: the wording of the research question suggest a two tailed tes. this means that the alternative or research hypothesis in step w will be stated as H sub 1: u does not equal 3.3 and that the critical region will be split between the upper and lower tails of the sampling distribution.)

Answer 1

Hypothesis Test for mean:

Assuming you have a large enough sample such that the central limit theorem holds, or you have a sample of any size from a normal population with known population standard deviation, then to test the null hypothesis

H0: μ ≤ Δ or

H0: μ ≥ Δ or

H0: μ = Δ

Find the test statistic z = (xbar - Δ ) / (sx / √ (n))

where xbar is the sample average

sx is the sample standard deviation, if you know the population standard deviation, σ , then replace sx with σ in the equation for the test statistic.

n is the sample size

The p-value of the test is the area under the normal curve that is in agreement with the alternate hypothesis.

H1: μ > Δ; p-value is the area to the right of z

H1: μ < Δ; p-value is the area to the left of z

H1: μ ≠ Δ; p-value is the area in the tails greater than |z|

If the p-value is less than or equal to the significance level α, i.e., p-value ≤ α, then we reject the null hypothesis and conclude the alternate hypothesis is true.

If the p-value is greater than the significance level, i.e., p-value > α, the significance level then we fail to reject the null hypothesis and conclude that the null is plausible.  Note that we can conclude the alternate is true, but we cannot conclude the null is true, only that it is plausible.

The hypothesis test in this question is:

H0: μ = 3.3 vs. H1: μ ≠ 3.3

The test statistic is:

z = ( 3.8 - 3.3 ) / ( 0.53 / √ ( 117 ))

z = 10.20439

The p-value = P( Z > |z| )

= P( Z < -10.20439 ) + P( Z > 10.20439 )

= 2 * P( Z < -10.20439 )

= 1.895074e-24

with such a small p-value we reject the null hypothesis and conclude the alternate is true.

Answer 2

If this was three years ago I could help you, but I've forgotten everything I learned in that class.

Answer 3

need more data like the number of students in the St algebra student body and the number of parties they attended.

Answer 4

From what I see, the answer would be no.  The random sample of 117 averages 3.8 parties, which is only one standard deviation from the mean.  If they averaged 4.86 parties, then they would be 2 SD from the mean.

You cannot reject the null hypothesis.