Question

2) On the Midterm Test, we examined data for a certain county regarding the relationship
between a teenager’s likelihood of going right to college after high school and whether or not
the teenager’s parent(s) had a college degree.
The data were as follows...
Group 1: One or more parents have a degree
Number of teenagers who went right to college = 212 Sample size = 398
Group 2: No parents previously completed a college degree
Number of teenagers who went right to college = 92 Sample size = 300
Do the data below support the claim that, for this county, the population proportion of
teenagers who attend college immediately after high school is higher among families where
one or more parents have completed a college degree? Conduct a hypothesis test to examine
this claim. Use a significance level of α = .02.
Assume all necessary conditions have been met for the test you choose.
To obtain full credit, your writing below should:
• Present the hypotheses to be evaluated (in symbols or words)
• Present and state the value of the test statistic you use (e.g., “Z =” or “t =”)
• Present a p-value based on that test statistic
• Clearly demonstrate a decision regarding the null hypothesis based on this p-value
• Answer the original question in a clear, concise, complete sentence (or sentences).

Answer 1

Null Hypothesis,H₀:the population proportions of teenagers who attend college immediately after high school is same for families where one or more parents have completed a college degree as the families with no prarent being graduated (ie)P₁=P₂

Alternative hypothesis,H_a:The population proportion of teenagers who attend college immediately after high school is higher among families where one or more parents have completed a college degree than the families without parents being graduate (ie)P₁>P₂

Level of significance =0.02

Test statistic is given as

Z=

Z=5.9614

p value is 0.000

Since p value is less than .05,then we reject H₀ and conclude that for this county, the population proportion of teenagers who attend college immediately after high school is higher among families where one or more parents have completed a college degree than the families without no parents being graduate