The null hypothesis is a principle in statistics that proposes there is no statistical correlation or significance among observed data sets. It assumes the proposed assertion to be accurate until it is disproven by statistical proof in the form of a hypothesis test. This concept is crucial for confirming the credibility of research conclusions.
| Topic | Problem | Solution |
|---|---|---|
| None | Identify the type I error and the type II error t… | In hypothesis testing, a type I error occurs when we reject a true null hypothesis, and a type II e… |
| None | The following sequence of 22 consecutive data val… | Given the sequence 1110011100001110101001, we have 10 zeros and 12 ones, and a total of 22 observat… |
| None | To test $\mathrm{H}_{0}: \sigma=2.3$ versus $\mat… | Given that the sample size \(n = 16\), the sample standard deviation \(s = 2.1\), and the standard … |
| None | According to a report, the standard deviation of … | The null hypothesis is a general statement or default position that there is no relationship betwee… |
| None | For students who firstenrolled in two-year public… | The null hypothesis is a statement of no effect or no difference. It is usually the hypothesis that… |
| None | A simple random sample of 10 pages from a diction… | Given that a simple random sample of 10 pages from a dictionary is obtained. The numbers of words d… |
| None | A simple random sample of 26 filtered $100-\mathr… | Given that the sample size (n) is 26, the sample standard deviation (s) is 0.20 mg, and the hypothe… |
| None | In a test of the effectiveness of garlic for lowe… | Identify the null and alternative hypotheses. The null hypothesis is that the mean change in LDL ch… |
| None | A data set about speed dating includes "like" rat… | Identify the null and alternative hypotheses. The null hypothesis (H0) is that the population mean … |
| None | Data on the numbers of hospital adimissions resul… | First, calculate the differences between the number of hospital admissions on Friday the 6th and Fr… |
| None | Trials in an experiment with a polygraph include … | Identify the null hypothesis and the alternative hypothesis. The null hypothesis is that the polygr… |
| None | A car company claims that its new SUV gets better… | Define the null hypothesis as the mean gas mileage of the company's SUVs being equal to the mean ga… |
| None | An article in the San Jose Mercury News stated th… | The student is conducting a one-tailed t-test to determine if the mean time to finish undergraduate… |
| None | Claim: The mean pulse rate (in beats per minute) … | The original claim can be expressed in symbolic form as \(\mu = 68.8\), where \(\mu\) represents th… |
| None | \begin{tabular}{|c|c|} \hline $\begin{array}{c}\t… | \(H_0: \beta_1 = 0\) (Square footage does not significantly affect the house price) |
| None | 1. Happy Acres Farm is considering spraying their… | State the null hypothesis (H0): \(\sigma^2 = 2.89\) cm², and the alternative hypothesis (H1): \(\si… |
| None | 3. Do different grades of gasoline affect mileage… | Calculate the F-statistic: \(F = \frac{590.49}{268.96} = 2.1955\) |
| None | You are a financial analyst for a brokerage firm.… | Calculate the F-test statistic: F = \(\frac{1.3^2}{1.16^2}\) |
| None | You are a financial analyst for a brokerage firm.… | Calculate the variances by squaring the standard deviations: \(variance_{NYSE} = 3.27^2 = 10.69\) a… |
| None | \( \times \) Question 9 Score on last try: 0 of 1… | \(p_1 = \frac{90}{180} = 0.5\) |
| None | Test the claim below about the mean of the differ… | \(H_0: \mu_d = 0, H_1: \mu_d \neq 0\) |