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# Some hypothesis testing problems

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Assume that a hypothesis test of the given claim will be conducted. The college Dean of Admissions claims that the times students require to earn a bachelors degree have a mean less than five years. Which equality/inequality (e.g., =, =<, etc.) would use in the Null Hypothesis?

Assume that a hypothesis test of the given claim will be conducted. The college Dean of Admissions claims that the times students require to earn a bachelors degree have a mean less than five years. Which equality/inequality (e.g., =, =<, etc.) would use in the Alternative Hypothesis?

The Hudson Valley Bottling Company distributes root beer in bottles labeled 32 ounces. The Bureau of Weights and Measures randomly selects 50 of these bottles, measures their contents and obtains a sample mean of 31.80 ounces with a standard deviation of 0.75 ounces (assume population values for mean and standard deviation). Using a 0.01 significance level, test the Bureaus claim that the company is cheating consumers. Indicate whether you would use a z score or t score, give the value of that score and the critical value to 2 decimal places, and state whether you "Reject" or "Fail to Reject" the null hypothesis. Example Answer: t, 1.45, 3.12, Reject

The skid properties of a snow tire have been tested and a mean skid distance of 154 feet has been established for standardized conditions. A new, more expensive tire is developed, but tests on a sample of 17 new tires yield a mean skid distance of 148 feet with a standard deviation of 12 feet. Because of the cost involved, the new tires will be purchased only if it can be shown (at the 0.005 significance level) that they skid less than the current tires. Based on the sample, will the new tires be purchased?Indicate whether you would use a z score or t score, give the value of that score and the critical value to 2 decimal places, and state whether you "Reject" or "Fail to Reject" the null hypothesis. Example Answer: z, 1.45, 3.12, Fail to Reject

In 1990, 5.8% of job applicants who were tested for drugs failed the test. At the 0.01 level, test the claim that the failure rate is now lower if a random sample of 1,520 current job applicants results in 58 failures. Does the result suggest that fewer job applicants now use drugs? Give the z score to 2 decimal places to, p(hat) to three decimal places, and the corresponding value of p to 4 decimal places. Also, do you conclude that fewer use drugs (Yes or No)? Example Answer: -2.21, 0.046, 0.0008, No

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#### Solution Preview

1. Assume that a hypothesis test of the given claim will be conducted. The college Dean of Admissions claims that the times students require to earn a bachelors degree have a mean less than five years. Which equality/inequality (e.g., =, =<, etc.) would use in the Null Hypothesis?

Null hypothesis
H0: The mean times students require to earn a bachelors degree ≥ 5 years
Alternative Hypothesis
H1: The mean times students require to earn a bachelors degree < 5 years

2. Assume that a hypothesis test of the given claim will be conducted. The college Dean of Admissions claims that the times students require to earn a bachelors degree have a mean less than five years. Which equality/inequality (e.g., =, =<, etc.) would use in the Alternative Hypothesis?

Null hypothesis
H0: The mean times students require to earn a bachelors degree ≥ 5 years
Alternative Hypothesis
H1: The mean times students require to earn a bachelors degree < 5 years

3. The Hudson Valley Bottling Company distributes root beer in bottles labeled 32 ounces. The Bureau of Weights and Measures randomly selects 50 of these bottles, measures their contents and obtains a sample mean of 31.80 ...

#### Solution Summary

Step by step method for testing the hypothesis under 5 step approach is discussed here. Excel template for each problem is also included. This template can be used to obtain the answers of similar problems.

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