eenage boys often complain that auto insurance costs more, on average, for teenage boys than for teenage girls. A group of concerned parents examines a random sample of insurance bills. The mean annual cost for 36 teenage boys was $679. For 23 teenage girls, it was $559. From past years, it is known that the population standard deviation for each group is $180. Determine whether or not you believe that the mean cost for auto insurance for teenage boys is greater than that for teenage girls under the assumption that auto insurance costs in the respective populations are normally distributed. For the conclusion, please use the following template. If you reject the null write Since p-value is [write the value of your p-value] and is less than [write the value of alpha in percent] we reject the null hypothesis at [write the value of alpha]% significance level. That is, there is sufficient evidence in the data to reject [write down the null hypothesis in the context of the problem]
Parents of teenage boys often complain that auto insurance costs more, on average, for teenage boys than for teenage girls. A group of concerned parents examines a random sample of insurance bills. The mean annual cost for 36 teenage boys was $679. For 23 teenage girls, it was $559. From past years, it is known that the population standard deviation for each group is $180. Determine whether or not you believe that the mean cost for auto insurance for teenage boys is greater than that for teenage girls under the assumption that auto insurance costs in the respective populations are
For the conclusion, please use the following template.
Since p-value is [write the value of your p-value] and is less than [write the value of alpha in
percent] we reject the null hypothesis at [write the value of alpha]% significance level.
That is, there is sufficient evidence in the data to reject [write down the null hypothesis in the
context of the problem]
If you fail to reject the null write
Since p-value is [write the value of your p-value] and is greater than [write the value of alpha in
percent], we fail to reject the null hypothesis at [write the value of alpha]% significance level.
That is, there is not sufficient evidence in the data to reject [write down null in the context of the
problem]
Please:
a) State the hypothesis.
b) Specify the type of test that we should use and justify your choice (there is no need to perform the hypothesis test and report the p-value.)
c) Explain if the assumption of normal distribution was essential for solving this question.
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