Question

The average monthly insurance bill for a college student is $32.79. A sample of 50 UD students finds that the pay $30.63. Using a population standard deviation of $5.60 and an alpha of 0.01 develop and test a Ho and Ha for this scenario and state your conclusion at the appropriate confidence level, in context, and in terms of the alternative hypothesis. You can use the p-value approach or the critical value approach

Answer 1

Given the average monthly insurance bill for a college student is = $32.79. A sample of n = 50 UD students finds that the pay an average bill of = $30.63. Using a population standard deviation of = $5.60 and an alpha of 0.01 the test is developed. based on the given claim tha Ho and Ha for this scenario is:

Based on the hypothesis this will be two-tailed test, since the population standard deviation is known and the sample size is greater than 30 hence it is assumed a normal distribution and Z statistic is applicable for hypothesis tesing.

P-value Approach

Rejection region:

Reject the Ho if P-value is less than 0.01

Test statistic:

P-value:

The P-value is computed using the excel formula for normal distribution which is =2*(NORM.S.DIST(-2.727, TRUE)), the P-value is computed as 0.0064.

Conclusion:

Since the P-value is less than 0.01 hence at 0.01 level of significance we reject the null hypothesis and conclude that there is sufficient evidence to warrant the rejection of the claim.