Statistics 11.1

A hospital director is told that 54% of the treated patients are insured. The director wants to test the claim that the percentage of insured patients is less than the expected percentage. A sample of 350 patients found that 175 were insured. State the null and alternative hypotheses.

H0: p=.54 Ha: p<.54

A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 447 gram setting. Is there sufficient evidence at the 0.05 level that the bags are underfilled? Assume the population is normally distributed. State the null and alternative hypotheses for the above scenario.

H0: μ=447 Ha: μ<447

An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 120 engines and the mean pressure was 5 lbs/square inch. Assume the variance is known to be 1. If the valve was designed to produce a mean pressure of 5.1 lbs/square inch, is there sufficient evidence at the 0.02 level that the valve performs below the specifications? State the null and alternative hypotheses for the above scenario.

H0: μ=5.1 Ha: μ<5.1

An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 110 engines and the mean pressure was 6.4 lbs/square inch. Assume the standard deviation is known to be 0.8. If the valve was designed to produce a mean pressure of 6.5 lbs/square inch, is there sufficient evidence at the 0.05 level that the valve does not perform to the specifications? State the null and alternative hypotheses for the above scenario.

H0: μ=6.5 Ha: μ≠6.5

An engineer has designed a valve that will regulate water pressure on an automobile engine. The valve was tested on 200 engines and the mean pressure was 7.7 lbs/square inch. Assume the standard deviation is known to be 0.8. If the valve was designed to produce a mean pressure of 7.6 lbs/square inch, is there sufficient evidence at the 0.02 level that the valve performs above the specifications? State the null and alternative hypotheses for the above scenario.

H0: μ=7.6 Ha: μ>7.6

A sample of 1500 computer chips revealed that 33% of the chips do not fail in the first 1000 hours of their use. The company's promotional literature states that 32% of the chips do not fail in the first 1000 hours of their use. The quality control manager wants to test the claim that the actual percentage that do not fail is different from the stated percentage. State the null and alternative hypotheses.

H0: p=.32 Ha: p≠.32

A sample of 800 computer chips revealed that 40% of the chips do not fail in the first 1000 hours of their use. The company's promotional literature claimed that more than 35% do not fail in the first 1000 hours of their use. Is there sufficient evidence at the 0.02 level to support the company's claim? State the null and alternative hypotheses for the above scenario.

H0: p=.35 Ha: p>.35

A sample of 1300 computer chips revealed that 32% of the chips fail in the first 1000 hours of their use. The company's promotional literature claimed that 35% fail in the first 1000 hours of their use. Is there sufficient evidence at the 0.02 level to dispute the company's claim? State the null and alternative hypotheses for the above scenario.

H0: p=.35 Ha: p≠.35

A sample of 1500 computer chips revealed that 41% of the chips fail in the first 1000 hours of their use. The company's promotional literature claimed that less than 44% fail in the first 1000 hours of their use. Is there sufficient evidence at the 0.02 level to support the company's claim? State the null and alternative hypotheses for the above scenario.

H0: p=.44 Ha: p<.44

The mayor of a town has proposed a plan for the construction of an adjoining bridge. A political study took a sample of 800 voters in the town and found that 55% of the residents favored construction. Using the data, a political strategist wants to test the claim that the percentage of residents who favor construction is more than 51%. State the null and alternative hypotheses

H0: p=.51 Ha: p>.51

A newsletter publisher believes that 62% of their readers own a personal computer. Is there sufficient evidence at the 0.05 level to refute the publisher's claim? State the null and alternative hypotheses for the above scenario.

H0: p=.62 Ha: p≠.62

A publisher reports that 65% of their readers own a laptop. A marketing executive wants to test the claim that the percentage is actually different from the reported percentage. A random sample of 130 found that 60% of the readers owned a laptop. State the null and alternative hypotheses.

H0: p=.65 Ha: p≠.65

A manufacturer of banana chips would like to know whether its bag filling machine works correctly at the 407 gram setting. Is there sufficient evidence at the 0.01 level that the bags are overfilled? Assume the population is normally distributed. State the null and alternative hypotheses for the above scenario.

H0: μ=407 Ha: μ>407

A manufacturer of chocolate chips would like to know whether its bag filling machine works correctly at the 435 gram setting. Is there sufficient evidence at the 0.02 level that the bags are underfilled or overfilled? Assume the population is normally distributed. State the null and alternative hypotheses for the above scenario.

H0: μ=435 Ha: μ≠435