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Statistics Hypothesis Tests for a Survey of Highschool Students who Work and Insurance Claims

1. A survey of 120 high school students shows that 39 of them work over 20 hours per week during the school year. Does it demonstrate the conjecture that more than 25% of the high school students work over 20 hours per week during the school year? ( Answer by calculating the P - value.)

2. Each year an insurance company reviews its claim experience in order to set future rates. Regarding their damage-only automobile insurance policies, at least one claim was made on 2073 of the 12,299 policies in effect for the year. Treat these data as a random sample for the population of all possible damage-only policies that could be issued.
(a) Test, at a level α = 0.05, the null hypothesis that the probability of at least one claim is 0.16 versus a two-sided alternative.
(b) Calculate the P - value and comment on the strength of evidence.

Solution Preview

Solution 1
Null Hypothesis , H0 : p = 0.25
Hence at 0.05 level, we conclude that the more than 25% of the High School students work over 20 ...

Solution Summary

The first solution in this response includes the Null Hypothesis, H0: p = 0.25. We find that at the 0.05 level, we can conclude that more than 25% of the High School students work over 20 hours per week during the school year. The second solution uses the Null Hypothesis, H0: p = 0.16, and uses the z-statistic. We reject the Null Hypothesis H0 if the P-value of z-statistic is less than 0.05. This solution is provided in an attached Word document.

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