Exam 10: Hypothesis Tests Based on a Single Sample

If a hypothesis test does not provide sufficient evidence to adequately support the alternative hypothesis, the most correct conclusion is:

A pharmaceutical company is considering the purchase of new bottling machines to increase its efficiency.The factory currently uses machines that fill cough syrup bottles whose volume of medicine has a standard deviation of 1.6 mL.The new machine the company is considering was tested on 30 bottles, producing a batch with a standard deviation of 1.25 mL.Does this machine produce a variance of less than 1.6 at the 0.05 significance level? State the TS and test decision.

A shoe salesman wishes to check the validity of his supplier's claim that the average length of the adult male foot is 9.34 in.He randomly samples 35 adult male customers and finds their average foot length to be 9.01 in.The standard deviation of foot length is known to be 0.75 in.What would be the test statistic for this test if the salesman thinks the supplier's claim is too high?

In an actual experiment, a researcher claims a drug cures a higher percentage of patients than the current therapy does.What is the null hypothesis, and why?

Suppose you reject the null hypothesis at the α = 0.01 significance level.Would you reject it at the α = 0.05 level?

An experimenter presented a body cue (such as bowing, pointing, or glancing) toward one of two objects and recorded whether a 4 year-old male collie named Krieger correctly chose the object indicated.Krieger chose the correct object 6 out of 10 times in this study.Does this provide evidence that Krieger understands human body cues? What are the TS, p-value, and decision in this study, using a 0.05 level of significance?

You have a SRS of size n = 16 from a normal distribution with σ = 1.You wish to test H₀: μ = 0 versus Ha: μ > 0.You decide to reject the null hypothesis if > 0 and not reject the null hypothesis otherwise.Find the probability of a type I error.

A shoe salesman wishes to check the validity of his supplier's claim that the average length of the adult male foot is 9.34 in.He randomly samples 35 customers and finds their average foot length to be 9.01 in.The standard deviation of foot length is known to be 0.75 in.What would be the critical value and decision for this test if the salesman thinks the supplier's claim is too high? (Use α = 0.01.)

You have a SRS of size n = 16 from a normal distribution with σ = 1.You wish to test H₀: μ = 0 versus Ha: μ > 0.You decide to reject the null hypothesis if > 0 and not reject the null hypothesis otherwise.Find the probability of a type II error when μ = 0.2.

A researcher claims that a new nose spray, formula N, is far more effective than that in use today, formula O.The null hypothesis should probably focus on

Suppose you wish to investigate whether your spun tennis racquet is equally likely to land with the label facing up or down.Does this study call for a one-sided or two-sided alternative?

Reports completed by independent truck drivers indicate that the mean amount of diesel fuel purchased per week is 346 gal, with a standard deviation of 23.6 gal.Truck managers use this information to plan work schedules and to order gasoline supplies.A random sample of 20 independent truck drivers was obtained and their average weekly gas purchases had a sample standard deviation of 11.7712 gal.Is there any evidence to suggest that the true population variance in diesel fuel purchased each week is different from 556.96? State the TS and decision from the test, using α = 0.05.

In a study of parents' perceptions of their children's size, researchers asked parents to estimate their youngest child's height.The researchers hypothesize that parents tend to underestimate their youngest child's size because the youngest child is the baby of the family and all other family members appear larger compared to the baby.The 39 parents who were surveyed underestimated their youngest child's height by 7.5 cm, on average; the standard deviation for the difference in actual heights and estimated heights was 0.72 cm, and the data were approximately normal.Which of the following is an appropriate null hypothesis for this study?

Which of the following is an appropriate hypothesis?

A professor wishes to discover if seniors skip more classes than do freshmen.Suppose he knows that freshmen skip 2% of their classes.He randomly samples a group of seniors.Out of 2521 classes, this group skipped 77 classes.Based on the sample, does it appear that seniors skip more than 2% of their classes? State the critical value (CV), test statistic (TS), and decision from the test.(Use α = 0.01.)

To test the effects of acid rain on the growth of white pine trees, a conservationist measures the diameter (in centimeters) of 200 white pines in the Allegheny National Forest in northwest Pennsylvania.The average diameter of the sampled trees is 23.42 cm.Does the sample provide sufficient evidence to conclude that the current mean diameter of the white pines is less than that recorded 50 years ago (μ = 24.8) if the standard deviation is 6 cm? Calculate the p-value and make an appropriate decision.(Use α = 0.05).

In any test of a hypothesis, to reject the null hypothesis is to:

A test of hypothesis has the following details: H₀: μ = 8000, Ha: μ > 8000, n = 50, σ = 409, α = 0.01, = 8158 Calculate the p-value and state the correct decision for this test.

The test statistic (TS) is:

The ___________ is an interval or set of numbers specified such that if the test statistic exceeds this limit, the status quo of H₀ is overturned.