5. A teacher wants to test his assumption that less than 30% of the Senior High
School students liked research class. After randomly collecting 150 samples,
he found out that only 40 students like their research class.
Claim:
Parameter
Symbol for parameter
Ho and Ha complementary pair.
Hypotheses in words:
Ho
Ha:
Hypotheses in symbols
Ho
На:
The population proportion "p" is the parameter.
Claim "p<0.3."
The following null and alternative hypotheses for the population proportion needs to be tested:
"H_0:" the population proportion is at least 30%.
"H_a:" the population proportion is less than 30%.
"H_0:p\\ge0.3"
"H_a:p<0.3"
This corresponds to a left-tailed test, for which a z-test for one population proportion will be used.
Based on the information provided, the significance level is "\\alpha = 0.05," and the critical value for a left-tailed test is "z_c =-1.6469."
The rejection region for this left-tailed test is "R = \\{z: z<-1.6469\\}."
The z-statistic is computed as follows:
Since it is observed that "z =-0.891>-1.6469=z_c," it is then concluded that the null hypothesis is not rejected.
Using the P-value approach:
The p-value is "p=P(Z<-0.891)=0.186465," and since "p = 0.186465 > 0.05=\\alpha," it is concluded that the null hypothesis is not rejected.
Therefore, there is not enough evidence to claim that the population proportion "p" is less than 0.3, at the "\\alpha = 0.05" significance level.
Comments
Leave a comment