Question

Astudy shoed 53% of college applications were submitted online. Assume this result is based on sa simple random sample of 1000 applications with 530 submitted online. Use 0.01 sig.level to test claim that among all student applications the percentage submitted online is equal to 50%.

Answer 1

Null hypothesis:
Ho: p = .50 -->meaning: population proportion is equal to .50
Alternative hypothesis:
Ha: p does not equal .50 -->meaning: population proportion does not equal .50

Using a formula for a binomial proportion one-sample z-test with your data included, we have:
z = (.53 - .50)/√[(.50)(.50)/1000]

Finish the calculation.

Use a z-table to find the critical values for a two-tailed test at .01 level of significance. Compare the test statistic calculated above to the critical values from the table. If the test statistic exceeds either critical value, reject the null and conclude p does not equal .50. If the test statistic does not exceed either critical value from the table, do not reject the null.

I hope this will help get you started.