Probability and Statistics: Hypothesis Testing One Sample
Calculate a T-statistic when the population standard deviation is unknown by using the sample standard deviation.
μ is 100 grams. An employee believes the mean is not 100 grams, forming the alternative hypothesis. Determine whether to use a one-tailed or two-tailed test for hypothesis testing.
Using the critical value approach to hypothesis testing, given an alpha level of 0.05, find the critical value on the standardized normal distribution curve where 5% of the area is in the tail.
A survey showed that the average male baby in the UK weighs 7 pounds 12 ounces at birth. A midwife in a Birmingham hospital suspects the birth weight may have increased in recent years and collects data to find out. Define the null and alternative hypotheses.
The vending machine should dispense bottles of water expected to contain 500 ml. A service engineer suspects that the actual amount in each bottle is less.
Define the null and alternative hypotheses.
Company XYZ manufactures calculators with an average mass of 450 grams. An engineer believes that average weight to be different and decides to calculate the average mass of 50 calculators. State the null and alternative hypotheses.
The teachers in a school believe that at least 80 percent of students will complete high school. A student disagrees with this value and decides to conduct a test. State the null and alternative hypotheses.
A teacher wishes to test if the average GPA of students in the high school is different from 2.7. State the null and alternative hypotheses.
The percentage of residents who own a vehicle in Town XYZ is no more than 75 percent. A researcher disagrees with the value and decides to survey 100 residents asking them if they own a vehicle. State the null and alternative hypotheses.
A random sample of 27 observations from a large population has a mean of 22 and a standard deviation of 4.8. Can we conclude at that the population mean is significantly below 24?
Suppose you run a website with an off-white background and the mean time spent on it is 20 minutes. You consider changing the background to yellow to increase time spent. Set up the null hypothesis that the change has no effect on the mean time, and an alternative hypothesis that the mean time is greater than 20 minutes due to the change. Using a sample size of 100, calculate the p-value when the sample mean time spent is 25 minutes. Determine if the null hypothesis can be rejected at a significance level of 0.05.
Assume John claims he has a technique that lets him roll a 6 more frequently than average using a special dice rolling technique. He rolls the dice a thousand times and gets a 6 in 20% of the cases. Given these results, determine if the findings are statistically significant by calculating the p-value.
A factory has a machine that dispenses 80 ml of fluid in a bottle. An employee believes the average amount of fluid is not 80 ml. Using 40 samples, he measures the average amount dispensed by the machine to be 78 ml with a standard deviation of 2.5. Part A: State the null and alternative hypotheses.
A company manufactures car batteries with an average lifespan of two or more years. An engineer believes this value to be less. Using 10 samples, he measures the average lifespan to be 1.8 years with a standard deviation of 0.5. Part A: State the null and alternative hypotheses.
A researcher is interested in finding out whether the average lifetime of females in the US is different from 75 years. For this, he takes a sample of 100 females with a sample mean of 76 and a sample standard deviation of 7. State the null and alternative hypotheses at a 95% confidence level. Is there enough evidence to reject the null hypothesis?
A researcher is interested in finding out whether the average regular gasoline price is higher than $2.45 in the Midwest region. The sample analyzed consists of 25 observations, a sample mean of 2.65, and a sample standard deviation of 0.35. State the norm and alternative hypotheses and, at a 99% confidence level, is there enough evidence to discard the null hypothesis?
In recent years, the mean age of all college students in city X has been 23. This year, a random sample of 42 students revealed a mean age of 23.8. Suppose their ages are normally distributed with a population standard deviation of 2.4. Can we infer at that the population mean age has changed?
Now, suppose we conduct this same test at 2% significance level. The null and alternative hypotheses are still the same. The significance level is 0.02. Dividing alpha into the two tails we have 0.01 in each tail. Looking this up in the t table, under .01 one tail or .02 2-tails, we see that the critical value is 2.326, which we can round to 2.33. Do we reject the null hypothesis at this significance level given the test statistic remains 2.16?