Exam 28: Inference for Decision Making

A newspaper poll asked respondents if they trusted "eco friendly" labels on Cleaning products. Out of 1000 adults surveyed, 498 responded "yes." We would like to Test if the proportion of respondents that trust these labels is at least 50%. The correct Alternative hypothesis is A. $\quad p = .50$ B. $\quad p \leq .50$ C. $\quad p \geq .50$ D. $p > .50$ E. $\quad p < .50$ Chapter 13: Calculate the appropriate test statistic.

A professor was interested in determining whether the prices of new textbooks in The bookstore were higher than if purchased online. She selected 6 textbooks and priced Each at the bookstore and online. Paired T-Test and CI: Bookstore, Online Paired $\mathrm{T}$ for Bookstore - online N Mean StDev SE Mean Bookstore 6 115.00 22.36 9.13 Online 6 105.83 13.20 5.39 Difference 6 9.17 13.20 5.39 95\% lower bound for mean difference: -1.69 T-Test of mean difference $=0(\mathrm{vs}>0): \mathrm{T}$ -Value $=1.70 \quad$ P-Value $=0.075$ Based on her analysis, we can conclude at the .05 level of significance that

Chris Columbus is responsible for controlling inventory levels for four types of Sailboats sold by his company. Chris takes a sample of 48 boats sold over the past Several months to determine if demand is the same for each type. His results are as Follows: Type of Boat Sales Pirate's Revenge 15 Jolly Roger 11 Sails Delight 10 Cruiser Cove 12 The calculated value of the Chi Square statistic is

A type I error is committed when

The weights of soy patties sold by Veggie Burgers Delight are normally Distributed. A random sample of 15 patties yields a mean weight of 3.8 ounces with a Sample standard deviation of 0.5 ounces. At the .05 level of significance, perform a Hypothesis test to see if the true mean weight is less than 4 ounces. The correct calculated value of the test statistic is

Suppose that a manufacturer is testing one of its machines to make sure that the Machine is producing more than 97% good parts $\left( H _ { 0 } : p = 0.97 \right.$ and $\left. H _ { A } : p > 0.97 \right)$ . The test results in a P-value of $0.102$ . In reality, the machine is producing $99 \%$ good parts. What probably happens as a result of our testing? A. We correctly fail to reject $H _ { 0 }$ . B. We correctly reject $H _ { 0 }$ . C. We reject $H _ { 0 }$ , making a Type I error. D. We fail to reject $H _ { 0 }$ , making a Type I error. E. We fail to reject $H _ { 0 }$ , making a Type II error.

A manufacturer of cordless electric shavers sampled 13 from a day's production And found the mean time of continuous usage without recharging to be 410 minutes with a sample standard deviation of 30 minutes. We can assume that times are normally Distributed. We wish to test if the true mean operating time without recharging is more Than 400 minutes. The correct calculated value of the test statistic is

A truck company wants on-time delivery for 98% of the parts they order from a Metal manufacturing plant. They have been ordering from Hudson Manufacturing But will switch to a new, cheaper manufacturer (Steel-R-Us) unless there is Evidence that this new manufacturer cannot meet the 98% on-time goal. As a test The truck company purchases a random sample of metal parts from Steel-R-Us, And then determines if these parts were delivered on-time. Which hypotheses Should they test? A. $\quad H _ { 0 } : p < 0.98$ $H _ { a } : p > 0.98$ B. $H _ { 0 } : p > 0.98$ $H _ { a } : p = 0.98$ C. $H _ { 0 } : p = 0.98$ $H _ { a } : p < 0.98$ D. $H _ { 0 } : p = 0.98$ $H _ { a } : p \neq 0.98$ E. $H _ { 0 } : p = 0.98$ $H _ { a } : p > 0.98$

A contact lens wearer read that the producer of a new contact lens boasts that their Lenses are cheaper than contact lenses from another popular company. The null hypothesis $H _ { 0 } : \mu _ { \text {old } } - \mu _ { \text {new } } = 0$ is tested against the alternative $H _ { A } : \mu _ { \text {old } } - \mu _ { \text {new } } > 0$ . Which of the following would be a Type II error?

We have created a 95% confidence interval for µ with the result (10, 15). What Conclusion will we make if we test $H _ { 0 } : \mu = 16 \text { versus } H _ { A } : \mu \neq 16 \text { at } \alpha = .05 ?$

After computing a confidence interval, the investigator believes that the results Are meaningless because the width of the interval is too large. In reconstructing the Interval, the investigator should

In economic downturns, companies attempt to downsize their workforces by Offering early retirement incentives to older employees. A survey of 723 companies Found that 195 engage in such downsizing practices. The 99% confidence interval for the Proportion of companies that downsize their workforces by offering early retirement Incentives is

Which of the following is not an assumption or condition that needs to be checked For a paired t-interval?

Which is true about a 99% confidence interval based on a given sample? I. The interval contains 99% of the population. II. Results from 99% of all samples will lie in this interval. III. The interval is wider than a 95% confidence interval would be.

A human resources manager at a large company wants to estimate the proportion Of employees that would be interested in reimbursement for college courses. If she Wishes to be 95% confident that her estimate is within 5% of the true proportion, how Many employees would need to be sampled?

A P-value indicates

A manufacturer of cordless electric shavers sampled 13 from a day's production And found the mean time of continuous usage without recharging to be 410 minutes with a sample standard deviation of 30 minutes. We can assume that times are normally Distributed. We wish to test if the true mean operating time without recharging is more Than 400 minutes. The correct null and alternative hypotheses are A. $\quad \mathrm { H } _ { 0 } : \mu = 400 ; \mathrm { H } _ { \mathrm { A } } : \mu < 400$ B. $\mathrm { H } _ { 0 } : \mu = 400 ; \mathrm { H } _ { \mathrm { A } } : \mu > 400$ C. $\mathrm { H } _ { 0 } : \mu > 400 ; \mathrm { H } _ { \mathrm { A } } : \mu = 400$ D. $\mathrm { H } _ { 0 } : \mu < 400 ; \mathrm { H } _ { \mathrm { A } } : \mu = 400$ E. $\mathrm { H } _ { 0 } : \mu = 400 ; \mathrm { H } _ { \mathrm { A } } : \mu \neq 400$

A newspaper poll asked respondents if they trusted "eco friendly" labels on Cleaning products. Out of 1000 adults surveyed, 498 responded "yes." We would like to Test if the proportion of respondents that trust these labels is at least 50%. The calculated Test statistic value is

We have calculated a 95% confidence interval and would like our next Confidence interval to have a smaller margin of error without losing any Confidence. In order to do this, we can I. change the $z ^ { * }$ value to a smaller number. II. take a larger sample. III. take a smaller sample.

The weights of soy patties sold by Veggie Burgers Delight are normally Distributed. A random sample of 15 patties yields a mean weight of 3.8 ounces with a Sample standard deviation of 0.5 ounces. At the .05 level of significance, perform a Hypothesis test to see if the true mean weight is less than 4 ounces. The correct null and alternative hypotheses are A. $\quad \mathrm { H } _ { 0 } : \mu = 4 ; \mathrm { H } _ { \mathrm { A } } : \mu > 4$ B. $\mathrm { H } _ { 0 } : \mu = 4 ; \mathrm { H } _ { \mathrm { A } } : \mu < 4$ C. $\mathrm { H } _ { 0 : } \mu > 4 ; \mathrm { H } _ { \mathrm { A } } : \mu = 4$ D. $\mathrm { H } _ { 0 } : \mu < 4 ; \mathrm { H } _ { \mathrm { A } } : \mu = 4$ E. $\quad \mathrm { H } _ { 0 } : \mu = 4 ; \mathrm { H } _ { \mathrm { A } } : \mu \neq 4$