Exam 9: One-Sample Hypothesis Tests

The process that produces Sonora Bars (a type of candy) is intended to produce bars with a mean weight of 56 gm. The process standard deviation is known to be 0.77 gm. A random sample of 49 candy bars yields a mean weight of 55.82 gm. Find the test statistic to see whether the candy bars are smaller than they are supposed to be.

As you are crossing a field at the farm, your country cousin Jake assures you, "Don't worry about that old bull coming toward us. He's harmless." As you consider Jake's hypothesis, what would be Type I error on your part?

A simultaneous reduction in both α and β will require a larger sample size.

The null hypothesis is:

In a right-tailed test, a statistician got a z test statistic of 1.47. What is the p-value?

The rejection region in a hypothesis test:

The hypotheses H₀: π ≥ .40, H₁: π < .40 would require:

A sample of 16 ATM transactions shows a mean transaction time of 67 seconds with a standard deviation of 12 seconds. State the hypotheses to test whether the mean transaction time exceeds 60 seconds.

Julia hypothesizes that fewer than 90 percent of her Visa purchases are under $100. She examines a random sample of her recent purchases and performs a test. The results shown below are from MegaStat. What would Julia conclude from this test? Explain carefully. Observed Hypothesized 0.8308 0.9 (as decimal) 108/130 117/130 (as fraction) 108. 117. 130 130 0.0263 std. error -2.63 z .0043 p-value (one-tailed, lower)

In a test of a mean, the reported p-value is .025. Using α =.05 the conclusion would be to:

In testing a proportion, which of the following statements is incorrect?

Last year, 10 percent of all teenagers purchased a new iPhone. This year, a sample of 260 randomly chosen teenagers showed that 39 had purchased a new iPhone. To test whether the percentage has risen, the critical value at α = .05 is:

In the nation of Gondor, the EPA requires that half the new cars sold will meet a certain particulate emission standard a year later. A sample of 64 one-year-old cars revealed that only 24 met the particulate emission standard. The test statistic to see whether the proportion is below the requirement is:

Other things being equal, a smaller standard deviation implies higher power.

Larger samples lead to increased power, ceteris paribus.

A two-tailed hypothesis test:

Mary examined a random sample of Friday withdrawals from a college campus ATM. She hypothesized that the mean was less than $100. The results shown below are from MegaStat. What would Mary conclude from this test? Explain carefully. Hypothesis Test: Mean vs. Hypothesized Value $100.000$ $\quad$$\quad$ hypothesized value $85.882$ $\quad$$\quad$ mean Withdrawal $85.078$ $\quad$$\quad$ std. dev. $20.634$ $\quad$$\quad$ std. error $17$$\quad$$\quad$$\quad$$\quad$ n 16 $\quad$$\quad$$\quad$$\quad$ df $- 0.68$$\quad$$\quad$$\quad$ t $.2518$$\quad$$\quad$ p-value (one-tailed, lower)

Compared to using α = .01, choosing α = .001 will make it less likely that a true null hypothesis will be rejected.

The Melodic Kortholt Company will change its current health plan if at least half the employees are dissatisfied with it. A trial sample of 25 employees shows that 16 are dissatisfied. For a right-tailed test, the test statistic would be:

For a given H_o and level of significance, if you reject the H₀ for a one-tailed test, you would also reject H₀ for a two-tailed test.