9.3/11.2 Quiz Hypothesis Testing (Differences )

To test the effects of a new fertilizer, 100 plots are treated with the new fertilizer, and 100 plots are treated with the old fertilizer. A computer’s random number generator is used to determine which plots get which fertilizer. the crops are weighed at the end of 6 weeks and mean weights from the two groups are compared.

Which kind of test should be used?

To test the effect of background music on productivity, fifty factory workers are observed. The number of tasks they complete are tallied. For one month, each subject works without music. For another month, the subject works while listening to music on an MP3 player. The month in which each subject listens to music is determined by a coin toss.

Which kind of test should be used?

It is thought that the average penny is older than the average quarter. The average age of a sample of 50 pennies was 8.72 years with a s = 0.73 years and the average age of 50 quarters was 6.78 years with a s = 0.99 years.

A major department store wants to compare the mean number of customers an employee can process per hour using two new scanning systems. 100 employees are randomly selected and then randomly assigned to one of the new systems. After each group of 50 has been trained on one scanning system and 50 on the other, the number of customers processed per hour is recorded. Which test is most appropriate for this situation?

A random sample of 425 citizens of Naboo found that 34% support the Galactic Republic. A sample of 585 citizens of Tatooine found that 38% support the Galactic Republic. What test would you use to assess a difference in support between Naboo and the Galactic Republic?

A Keebler sales rep claims that there are more chocolate chips in their cookie than in Chips Ahoy cookies.  You take a random sample of 20 Keebler cookies and find an average of 15.8 chips per cookie and a s = 3.7 chips. A random sample of 25 Chips Ahoy yields 14.2 chips per cookie and s = 4.3 chips. Suppose Ho: $$\mu_k-\mu_a=\ 0$$ and Ha: $$\mu_k-\mu_a>0$$ What is the conclusion of the test at the 5% level of significance?

A researcher was interested in comparing the salaries of female and male employees of a particular company. Independent random samples of 8 female employees and 15 male employees yielded the following weekly salaries (in dollars). Ho: μ_F - μ_M = 0 and Ha: μ_F - μ_M $$<$$ 0. What does the alternative hypothesis say in context?

A researcher was interested in comparing the salaries of female and male employees of a particular company. Independent random samples of 8 female employees and 15 male employees yielded the following weekly salaries (in dollars). Ho: μ_F - μ_M = 0 and Ha: μ_F - μ_M $$<$$ 0. Find the p-value (Rounded to the nearest three decimal places).

In a random of 850 city high school students, 768 said they had access to the internet during school hours. 308 of 355 rural high school students said they had access. The null and alternative hypotheses are as follows: Ho: $$p_c=p_r$$ and Ha: $$p_c\ne p_r$$ . Select ALL significance levels, if any, under which you would you reject the null. (Calculate the p-value to determine your answer. )

Jimmy is interested in comparing the fitness level of the members of his gym to the levels at a competing gym. He randomly selected 125 members of his gym and found 75 passed a fitness test. 70 of 95 at the other gym passed. The 95% interval (-0.26, -0.013) gives an estimate for the true difference in proportion of members in Jimmy's gym who can pass the test and the proportion from the other gym who can pass. Use this interval to make your conclusion about the hypothesis test of Ho: $$p_1=p_2$$ Ha: $$p_1\ne p_2$$ .