1) Make the decision about the given claim. Don’t use any formal procedures and exact calculation. Use only the rare event rule.
Claim: A coin favors head when tossed, and there are 8 heads in 18 tosses.
2) Make the decision about given claim. Use only rare event rule, and make subjective estimates to find out whether events are likely. Like if the claim is that a coin favours heads and sample results consist of 11 head in 20 flips, conclude that there is not enough evidence to support claim that the coin favors heads (because it is easy to get 11 heads in 20 flips by chance with a fair coin).
Claim: Mean pulse rate (in beats per minute) of students in a large statistics class is greater than 66. Simple random sample of the students has a mean pulse rate of 66.3.
3) Observe the given statement, then express null hypothesis H0 and the alternative hypothesis H1 in symbolic form. The mean weight of women who won a beauty pageant is equal to 119 lb. Which formula is the hypothesis test to be conducted?
4) Suppose that the normal distribution applies and find the critical z value(s).
A = 0.04; H1 is mean ≠ 98.6 degrees Fahrenheit.
5) Find the value of the test statistic z using z = proportion-p Divided by √pq Divided by N
The claim is that the proportion of peas with yellow pods is equal to 0.25 (or 25%). The sample statistics from one experiment include 400 peas with 96 of them having yellow pods.
6) Use information given below to determine the P-value. Also, use a 0.05 significance level and state the conclusion about null hypothesis (reject null hypothesis or fail to reject null hypothesis).
The test statistic in a left-tailed test is z = - 1.88.
What is the P-value: (Round to four decimal places as required)
7) Use the given information to find the P-value. The test statistic in a two-tailed test is z = 1.49 P-value = (round to four decimal places as needed)
8) For the following claim, determine null and alternative hypotheses, test statistic, P-value, critical value and illustrate the conclusion. Suppose that a simple random sample has been selected from a normally distributed population.
Claim: The mean IQ score of statistics professors is greater than 130.
Sample data: n = 12, mean = 134, s= 10. The significance level is a = 0.05.
a) Select the correct null hypotheses (H0) and alternative hypothesis (H1).
9) Suppose that simple random sample has been chosen from a normally distribute population and test the given claim. Recognize the null and alternative hypotheses, test statistic, P-value, critical value(s), and state the final conclusion that addresses the original claim.
In a manual on how to have a number one song, it is stated that a song should be no longer than 210 seconds. A simple random sample of 40 present hit songs results in a mean length of 242.2 sec and a standard deviation of 53.81 sec. Use a 0.05 significance level and the accompanying Minitab display to test the claim that the sample is from a population of songs with a mean greater than 210 sec. What do these results suggest about the advice given in the manual?
Minitab display
One-Sample T
Test of mu = 210 vs> 210
N 40 Mean 242.20 StDev 53.81 SE Mean 8.51 95% Lower Bound 227.86 T 3.78 P 0.000
What are the hypotheses?
10) Test the following claim. Identify the null hypothesis, alternative hypothesis, test statistic, critical value(s), conclusion about the null hypothesis, and final conclusion that address the original claim.
A manual states that in order to be a hit, a song must be no longer than three minutes and ten seconds (or 190 seconds). A simple random sample of 45 current hit songs results in a mean length of 255.0 sec. Assume the population standard deviation of song lengths is 53.5 sec. Use a 0.05 significance level to test the claim that the sample is from a population of songs with a mean greater than 190 sec. What do these results suggest about the advice given in the manual?
What are the null and alternative hypotheses?
Stating Conclusions About Claims.
11) Use only the rare event rule, and make subjective estimates to determine whether events are likely. For ex, if the claim is that a coin favors heads and sample results consist of 11 heads in 20 flips, conclude that there is not sufficient evidence to support the claim that the coin favors heads (because it is easy to get 11 heads in 20 flips by chance with a fair coin).
Claim: Movie patrons have IQ scores with a standard deviation that is less than the standard deviation of 15 for the general population. A simple random sample of 40 movie patrons results in IQ scores with a standard deviation of 14.8.