Exam 12: Hypothesis Testing: Describing a Single Population

The manager of a fast food restaurant is investigating the average number of fries per Large-sized offered to customers, to assess quality control. The manager took a random sample of five Large-sized orders of fries, and counted the number of fries per serve, with the results given below: 73 75 83 68 78 Assume that the number of French fries served at this fast food restaurant is normally distributed. Can we infer at the 5% significance level that the average number of fries served in a Large-sized order of fries at this fast food restaurant is over 70?

An alternative or research hypothesis is an assertion that holds if the null hypothesis is false.

During the Gulf War, a government official claimed that the average car owner refilled the fuel tank when there was more than 3 litres of petrol left. To check the claim, 10 cars were surveyed as they entered a service station. The amount of petrol (in litres) was measured and recorded as shown below. 3 5 3 2 3 3 2 6 4 1 Assume that the amount of petrol remaining in the tanks is normally distributed with a standard deviation of 1 litre. a. Calculate the p-value. b. Compute the probability of a Type II error if the true average amount of gas remaining in tanks is 3.5 litres.

Given that s = 15, n = 50, $\bar { X }$ = 17.5, α = 0.05, test the following hypotheses: H0: μ = 22 HA: μ ≠ 22

If the value of the sample mean $\bar { X }$ is close enough to the hypothesised value of the population mean ? , then:

In testing the hypotheses H0: μ = 60 HA: μ < 60 the following information was given:  = 5, n = 100, $\bar { X }$ = 59, α = 0.05. a. Calculate the value of the test statistic. b. Set up the rejection region. c. Determine the p-value. d. Interpret the result.

The power of a test is the probability that a true null hypothesis will be rejected.

Determine the p-value associated with each of the following values of the standardised test statistic z. a. Two-tail test, Z = 1.50. b. One-tail test, Z = 1.05. c. One-tail test, Z = -2.40.

Suppose that nine observations are drawn from a normal population whose standard deviation is 2. The observations are: 15 9 13 11 8 12 11 7 10 At 95% confidence, you want to determine whether the mean of the population from which this sample was taken is significantly different from 10. a. State the null and alternative hypotheses. b. Compute the value of the test statistic. c. Compute the p-value. d. Interpret the results.

Whenever the null hypothesis is not rejected:

Suppose that we reject a null hypothesis at the 0.05 level of significance. For which of the following $\alpha$ -values do we also reject the null hypothesis?

When using a t-test to test the population mean, the degrees of freedom is n - 1.

If we reject the null hypothesis, we conclude that there is enough statistical evidence to infer that the alternative hypothesis is true.

In any given test, it is possible to commit the Type I and Type II errors at the same time.

The power of a test is denoted by:

If we reject the null hypothesis, we conclude that:

The p-value is usually 0.05.

If we do not reject the null hypothesis, we conclude that there is enough statistical evidence to infer that the null hypothesis is true.

A two-tail test for the population mean  produces a test-statistic Z = -1.43. The p-value associated with the test is 0.0764.

In a one-tail test, the p-value is found to be equal to 0.018. If the test had been two-tail, the p-value would have been 0.036.