Statistics and Probability Answers

above what value of inside diameter will 10% of the piston rings fall?

A manufacturer of tires claim that their tire has a mean life of at least 50,000kms. A random sample of 28 of these tires is tested and the sample mean is 33,000kms. Assume that the population standard deviation is 3,000kms and the lives of the tires are approximately normally distributed.

In a recent survey a researcher claimed that on average filipino teenagers watch k-dramas for 3.5 hours daily is the claim correct if a random sample of 50 filipino teenagers showed a mean of 2.8 hours with a standard deviation of 0.9 hours? use 99% confidence level

A group of students got the following scores in a test: 6,9,13,16,18,21. Consider sample size of size 3 that can be drawn from this population.

A. List all the possible samples and the corresponding mean.

B. Construct the samplong distribution of the sample means.

C. Compute for the mean and standard deviation of the sampling distribution of the sample means.

A manufacturing firm claims that each water bottle they produce contains an average of 300 mL of water with a standard deviation of 1.2 mL. A random sample of 20 water bottles showed an average volume of 301.4 mL. if the t-value in the test is 3.14 and the critical values are ±2.861, what is the appropriate decision conclusion in the hypothesis testing?

According to a student conducted by the grade 12 students P155 is the average monthly expense for cellphone loads of high school students in their province. A statistics student claims that this amount has increased since January of this year. do you think his claim is acceptable if a random sample of 50 students has an average monthly expense of P165 for cellphone loads? Using 5% level of significance, assume that a population standard deviation is P52

2. An association of City Mayors conducted a study to determine the average number of times a family went to buy necessities in a week. They found that the mean is 4 times in a week. A random sample of 20 families were asked and found a mean of 5 times in a week and a standard deviation of 2. Use 5% significance level to test that the population mean is not equal to 5. Assume that the population is normally distributed

A medical expert claims that 80% of recovered COVID-19 patients have produced antibodies against the virus. To verify this, 1,000 recovered patients were tested and found that 823 of them have antibodies for the corona virus. Is this enough evidence to support the claim? Use 𝑎 = 0.01.

A politician claims that he will get at least 70% of the votes. Out of 300 randomly sampled registered voters, 200 said they will vote for the said politician. Test the claim using 0.10 level of significance.