The life expectancy of a dog has a mean of 12 years with a variance of 4 years2. The life expectancies of 64 dogs were collected and the sample mean was measured at 11.5 years. Please compute the p-value for the relevant hypothesis test to check whether the mean value is 12 years.Please round your result to 2 decimal places.
Question
The life expectancy of a dog has a mean of 12 years with a variance of 4 years2. The life expectancies of 64 dogs were collected and the sample mean was measured at 11.5 years. Please compute the p-value for the relevant hypothesis test to check whether the mean value is 12 years.Please round your result to 2 decimal places.
Solution
To solve this problem, we need to conduct a one-sample z-test. Here are the steps:
-
State the null hypothesis and the alternative hypothesis. Null hypothesis (H0): μ = 12 Alternative hypothesis (H1): μ ≠ 12
-
Calculate the standard deviation (σ) from the variance. The standard deviation is the square root of the variance, so σ = sqrt(4) = 2.
-
Calculate the standard error (SE). The standard error is the standard deviation divided by the square root of the sample size (n). So, SE = σ / sqrt(n) = 2 / sqrt(64) = 2 / 8 = 0.25.
-
Calculate the z-score. The z-score is the difference between the sample mean (x̄) and the population mean (μ) divided by the standard error. So, z = (x̄ - μ) / SE = (11.5 - 12) / 0.25 = -2.
-
Look up the p-value associated with the calculated z-score. The p-value associated with a z-score of -2 (two-tailed) is approximately 0.0455.
So, the p-value for the hypothesis test is approximately 0.05 (rounded to two decimal places). This p-value is less than the common significance level of 0.05, so we would reject the null hypothesis and conclude that there is evidence to suggest that the mean life expectancy of dogs is not 12 years.
Similar Questions
Suppose a manufacturer wants to estimate the averagelifespan of a new product they have developed. Theyrandomly select 15 products and test them until they fail.It is known that the average lifespan is 120 hours, with astandard deviation of 10 hours. Assume that the lifespanof the products follows a normal distribution. Themanufacturer wants to know the probability that theaverage lifespan of the product is greater than 130 hours.
The quality-control manager at a compact fluorescent light bulb(CFL)factory needs to determine whether the mean life of a large shipment of CFLs is equal to 7450 hours.The population standard deviation is 990 hours.A random sample of 81 light bulbs indicates a sample mean life of 7,252 hours. At the 0.05 level of significance.is there evidence that the mean life is different from 7450 hours? What is the test statistic?
years; the standard deviation is years.Use the empirical rule to estimate the probability of a gorilla living longer than years.
Suppose that the lifetimes of old-fashioned TV tubes are normally distributed with a standard deviation of 1.2 years. Suppose also that exactly 40% of the TV tubes die before 4 years. Find the mean lifetime of TV tubes. Carry your intermediate computations to at least four decimal places. Round your answer to at least one decimal place.years
A quality control expert at Glotech computers wants to test their new monitors. The production manager claims they have a mean life of 8989 months with a standard deviation of 55 months.If the claim is true, what is the probability that the mean monitor life would be greater than 87.887.8 months in a sample of 123123 monitors? Round your answer to four decimal places.
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.