Ferris State University Michigan College The Hypothesis Test using the P Value Method Paper - Mathematics
few questions related to hypothesis. State the null and alternative hypotheses symbolically.Find the Test Statistic.Calculate the p-Value.State the initial decision.State the conclusion in terms of the original claim.
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The 5-steps of a Hypothesis Test using the p-Value Method:
1. State the null and alternative hypotheses symbolically.
2. Find the Test Statistic.
3. Calculate the p-Value.
4. State the initial decision.
5. State the conclusion in terms of the original claim.
Example #1 Large Sample Hypothesis Test for the Mean:
A researcher wishes to test the claim that the average cost of tuition and fees at a local
community college is greater than $5700. She selected a random sample of 36 college
students and finds the mean to be $5950 and the standard deviation to be $659. Use the pValue method to test her claim at alpha=0.05.
1. A researcher claims that the average wind speed in a certain city is 8 miles per hour. A
sample of 32 days has an average wind speed of 8.2 miles per hour and a standard deviation
of 0.6 miles per hour. Use the p-Value method to test the claim at alpha=0.05.
2. The mean salary of federal government employees is $59593. The average salary of 30
randomly selected state employees is $58800 with a population standard deviation of $1500.
At the 0.01 level of significance, can it be concluded that the state employees earn an average
less than the federal employees. Use the p-Value method.
Example: Small Hypothesis Test for the Mean:
A medical investigation claims that the average number of infections per week at a hospital is
16.3. A random sample of 10 weeks had a mean number of 17.7 infections. The sample
standard deviation is 1.8. Is there enough evidence to reject the investigator’s claim at
alpha=0.05? Assume that the variable is normally distributed. Use the p-Value method.
3. The average salary of a nurse in a certain city is $79500. A researcher wishes to test the
claim that the average starting salary of nurses in this city is less than $79500. A random
sample of 8 starting nurses is selected, and their salaries are shown below. Is there enough
evidence to support the researcher’s claim at alpha=0.10? Assume the variable is normally
distributed. Use the p-Value method.
82000 68000 70200 75600 83500 64300 78600
79000
4. An author claims that the average novel is at least 50,000 words. A writing club
randomly selected seven novels that have a mean length of 50,364 words. Suppose it is
know the standard deviation of the population is 1,113. At a 10\% significance level is there
sufficient evidence to conclude that the mean length is greater than 50,000 words? Use the
p-Value method.
Example: Hypothesis Test for the Proportion:
An official at the Treasury believes less than 20\% of the population prefers using $1 coins as
opposed to $1 bills. To see if this claim is valid a random sample of 80 people were
surveyed and found that 8 preferred using $1 coins At alpha=0.01, test the claim that less
than 20\% of the population prefer using $1 coins as opposed to $1 bills. Use the p-Value
method.
5. An attorney claims that more than 25\% of all lawyers advertise. A random sample of 200
layers showed that 63 had used some form of advertisement. At alpha=0.05, is there enough
evidence to support the attorney’s claim. Use the p-Value method.
6. A doctor claims that, based on observation, 17\% of young people ages 3-18 are obese. To
test the claim the doctor randomly selects 200 people ages 3-18 and found that 42 were
deemed to be obese. At alpha=0.05, is there enough evidence to reject the claim? Use the pValue method.
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