To testH0 :μ=105versusH1 :μ̸=105,asimplerandomsampleofsizen=25is obtained. (a) If x ̄ = 101.9 and s = 5.9, compute the test statistic. (b) Draw a t-distribution with the area that represents the p-value shaded. (c) Approximate and interpret the p-value. (d) If the researcher decides to test this hypothesis at the α = 0.01 level of significance, will the researcher reject the null hypothesis? Why?

To testH0 :μ=105versusH1 :μ̸=105,asimplerandomsampleofsizen=25is obtained. (a) If x ̄ = 101.9 and s = 5.9, compute the test statistic. (b) Draw a t-distribution with the area that represents the p-value shaded. (c) Approximate and interpret the p-value. (d) If the researcher decides to test this hypothesis at the α = 0.01 level of significance, will the researcher reject the null hypothesis? Why?

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter13: Probability And Calculus

Section13.3: Special Probability Density Functions

Problem 30E

See similar textbooks

Similar questions

A company has a new process for manufacturing large artiﬁcial sapphires. In a trial run, 37 sapphires are randomly selected. The mean weight for these gems is x¯=6.75 carats, and the sample standard deviation is s=0.33 carat. Let μ be the mean weight for the distribution of all sapphires produced by the new process. What is the degrees of freedom in this problem? Use table or Technology to find t-critical value with degrees of freedom found above and with α=0.05 significance level. Find the Margin of error (E) Find a 95% confidence interval for μ Interpret the conﬁdence interval in the context of the problem.
The analytic scores on a standardized aptitude test are known to be normally distributed with mean μ = 610 and standard deviation o = 115. (a) Draw a normal curve with the parameters labeled. Shade the region that represents the proportion of test takers who scored less than 725. (b) Suppose the area under the normal curve to the left of X = 725 is 0.8413. Provide an interpretation of this result.
About % of the area under the curve of the standard normal distribution is between z=−2.031z=-2.031 and z=2.031z=2.031 (or within 2.031 standard deviations of the mean).
What is the kurtosis for the distribution of scores with a mean of 9.02 and a mode of 3?
An independent random sample is selected from an approximately normal population with an unknown standard deviation. Find the p-value for the given sample size and test statistic. Also determine if the null hypothesis would be rejected at α = 0.05. For each the given set of hypotheses, sample size and the T-statistic,find the p-value, draw a t-curve and shade the region of which the area the p-value indicates. As it’s notpossible to find the precise P-values using a t-table, it suffices to give a range. (a) HA : μ 6= 0.5, n = 26, T = 2.6(b) HA : μ < 3, n = 18, T = −2.2(c) HA : μ < 3, n = 18, T = 2.2
The mean life span of caterpillars before becoming butterflies is 4.75 months with a population standard deviation of 0.39 months. A caterpillarologist thinks the average life span of monarch caterpillars is different from 4.75 months. The scientist collects a sample of 50 monarch caterpillars that have a mean life span of 4.85 months. Test the claim at α = .01. (BY HAND) SHOW WORK PLEASE.
Find the least square estimate for beta (the slope) given that its y-intercept is 0. Y_i = BetaX_i + e_i where e_i are independent and identically distributed N(0, variance_e) randon variables i = 1,...,2.
Pressure values measured by various probes in the test section of a wind tunnel to obtain the freestream velocity have been given in the table below. The researcher who made the measurements concluded that the 7th reading had a value of -2.567 as the "deviation from the mean" and eliminated the data point based on the Chauvenet criterion. However, she later realized that she used the factor "1/n" instead of "1/(n-1)" in the calculation of standard deviation, which was used for data sets with a total number of data points less than 20. Find the value of the 7th reading. n=1 p=246 n=2 p=240 n=3 p=242 n=4 p=245 n=5 p=245 n=6 p=242 n=7 p=? n=8 p=244 n=9 p=244
uestion 34. After having made a decision on the test at the significance of a = 0.05, the most ppropriate conclusion in the context of research is A) There is not any significant difference between the species with respect to population mean brain eptide content. B) There is a significant difference between the species with respect to population mean brain peptide ontent. C) The population mean brain peptide content of skate fish is significantly greater than that of dogfish. D) The population mean brain peptide content of skate fish is not significantly greater than that of dogfish. E) The population mean brain peptide content of skate fish is exactly the same as that of dogfish. Questions 35-36. The information about head sizes was collected over 18 pilots to determine the feasibility of using cheap cardboard callipers to make the measurements, instead of metal ones which were expensive and uncomfortable. The head size of each pilot was measured once using a cardboard calliper and…
We collected a sample of twenty-five observations. We assumed that the observations are from a population whose values follow a normal distribution with a mean of u and a standard deviation of five. We performed a test with these hypotheses Ho: μ = 0H₁ = 0 and H₁ : μ0H₁0. The test statistic is the sample mean . The 5% rejection region is 1.959964 > 1.959964. What is the power of this test when μ = -2μ = -2? Please state the statistical power up to the fourth decimal place.
A light bulb manufacturer guarantees that the mean life of a certain type of light bulb is at least 735 hours. A random sample of 26 light bulbs has a mean life of 710 hours. Assume the population is normally distributed and the population standard deviation is 59 hours. At α=0.05, do you have enough evidence to reject the manufacturer's claim? Identify Ho and Ha find the critical value(s) and sketch region calculate the test statistic and add it to the sketch Do you reject the Ho or fail to reject Ha
A new process for producing synthetic diamonds can be operated at a profitable level only if the average weight of the diamonds is greater than 0.5 karat. Sixteen diamonds are generated, with a mean weight of 0.5457 karat and sample standard deviation equals 0.0552 karat. Assuming that the data is normal and using α=0.10, test if the data support the claim that the process is profitable. Group choices p-value=0.2, evidence not support claim p-value=0.373, evidence support claim p-value=0.373, evidence not support claim p-value=0.02, evidence support claim p-value=0.002, evidence support claim