A survey claims that 9 out of 10 doctors (i.e., 90%) recommend brand Z for their patients who have children. To test this claim against the alternative that the actual proportion of doctors who recommend brand Z is less than 90%, a random sample of 100 doctors results in 94 who indicate that they recommend brand Z. The test statistic in this problem is approximately:

Express the null hypothesis and the alternative hypothesis in symbolic form. Use the correct symbol (μ , ρ, σ) for the indicated parameter. An entomologist writes an article in a scientific journal which claims that fewer than 9 in ten thousand male fireflies are unable to produce light due to a genetic mutation. Use the parameter p, the true proportion of fireflies unable to produce light.

Assume that a hypothesis test of the given claim will be conducted. Identify the type I or type II error for the test. A skeptical paranormal researcher claims that the proportion of Americans that have seen a UFO, p, is less than 5 in every one thousand. Identify the type II error for the test.

An article reports that 34% of American fathers take no responsibility for child care. A researcher claims that the figure is higher for fathers in the town of Littleton. A random sample of 225 fathers from Littleton, yielded 97 who didn’t help with child care. Find the P- value for a test of the researcher's claim.

Find the critical t-value or values for the given hypothesis, sample size, and significance level. H1: μ >3.74, n = 13, α = 0.01.

Given the claim μ ≤ 85 and P -value= 0.004, do you reject or fail to reject H0 at the 0.01 level of significance?

Formulate the indicated conclusion in nontechnical terms. Be sure to address the original claim. The manufacturer of a refrigerator system for beer kegs produces refrigerators that are supposed to maintain a true mean temperature, μ, of 50°F, ideal for a certain type of German pilsner. The owner of the brewery does not agree with the refrigerator manufacturer, and claims he can prove that the true mean temperature is incorrect. Assuming that a hypothesis test of the claim has been conducted and that the conclusion is to reject the null hypothesis, state the conclusion in nontechnical terms.

Top management of a large multinational corporation wants to create a culture of innovativeness and change. A consultant hired to assess the company's organizational culture finds that only 15% of employees are open to new ideas and approaches toward their work. Consequently the company conducts a program for employees in order to reinforce the new corporate philosophy. Based on data collected after the program, the finds the 95% confidence interval for the proportion of all employees open to new ideas to be 18% to 22%. What should the company conclude? I. The null hypothesis should not be rejected. II. There is no evidence to suggest that the program improved employees' attitudes toward innovativeness and change. III. There is evidence that the program improved employees' attitudes toward innovativeness and change.

A cereal company claims the mean weight of the cereal in its packages is at least 14 oz. You wish to test this claim at α = 0.02 level of significance. The mean weight for a random sample n= 12 cereal packets is 13.4 oz with a sample standard deviation of 0.8 oz. Compute the value of an appropriate test statistic for the given hypothesis test.

For the set of hypotheses, use the sample information to compute the appropriate test statistic. H0: σ = 8.3 α = 0.02 n = 50 s = 7.2 H1: σ ≠ 8.3 The sample is from a normal distribution.