Question

1. In a clinical study of an allergy drug, 108 of the 203 subjects reported experiencing significant relief from their symptoms. Using a significance level of 0.01, test the claim that more than half of all those using the drug experienced relief. State the null hypothesis H0. State the alternative hypothesis H1. What is the test statistic? State the alpha level. Determine p value. Do you or do you not reject the null hypothesis? Why? Write a clear conclusion using a complete sentence.
2. According to a recent poll, 53% of Americans would vote for an incumbent president. If a sample of 100 people results in 45% who would vote for the president to be incumbent, test the claim that the percentage is 53%. Use a 0.10 significance level. State the null hypothesis H0. State the alternative hypothesis H1. What is the test statistic? State the alpha level. Determine p value. Do you or do you not reject the null hypothesis? Why? Write a clear conclusion using a complete sentence.
3. A public bus company official claims that the mean waiting time for bus number 14 during peak hours is less than 10 minutes. Karen took bus 14 during peak hours on 18 different occasions. Her mean waiting time was 7.4 minutes. Assume the standard deviation has been historically known to be 2.2 minutes. At the 0.05 significance level, test the claim that the mean waiting time is less than 10 minutes. State the null hypothesis H0. State the alternative hypothesis H1. What is the test statistic? State the alpha level. Determine p value. Do you or do you not reject the null hypothesis? Why? Write a clear conclusion using a complete sentence.
4. The world’s smallest mammal is the bumblebee bat. Such bats are roughly the same size of a large bumblebee. Listed below are the weights (in grams) from a sample of these bats. Assuming that all such bats have a standard deviation of 0.3 grams, use a significance level of 0.05 to test the claim that these bats are from the same population with a mean of 1.8 grams. Do the bats appear to be from the same population? You may assume the sample data comes from a population that follows a normal distribution. State the null hypothesis H0. State the alternative hypothesis H1. What is the test statistic? State the alpha level. Determine p value. Do you or do you not reject the null hypothesis? Why? Write a clear conclusion using a complete sentence. 2.13 1.31 1.91 1.92 1.77 1.64   2.29 1.99 2.33   2.49   2.22
5. A manufacturer makes steel rods that are supposed to have a mean length of 50 centimeters. A retailer suspects that the bars are being produced too short. A sample of 46 bars is taken and their mean length is determined to be 51 centimeters with a standard deviation of 3.6 centimeters. Using a 0.01 significance level, test the retailers claim that the population mean is less than 50 centimeters. State the null hypothesis H0. State the alternative hypothesis H1. What is the test statistic? State the alpha level. Determine p value. Do you or do you not reject the null hypothesis? Why? Write a clear conclusion using a complete sentence

Answer 1

1. In a clinical study of an allergy drug, 108 of the 203 subjects reported experiencing significant relief from their symptoms.

Let "p' be the proportion of subjects experiencing significant relief from their symptoms.

Therefore, the estimate of p is:

P = 203 = 0.53 = 108

At 1% level of significance, we want to test the claim that more than half of all those using the drug experienced relief.

The hypothesis are:

Null Hypothesis:

Ho :p < 0.50

Alternative hypothesis:

H1 :p> 0.50

The test statistic is:

2= P-p p(1-p)

之- 0.53 -0.50 10.50+(1-0.50) 2US

0.03 0.50*0.50 V 203

0.03 0.00123

10.03 10,03507

= 0,855

q=0.86

The p value for the upper tailed test is:

p= P(Z > 0.86

p= [1 - P(Z <0.86)

          ### By using z table:

p=1-0.8051

p=0.1949

Since p value >0.01, we are unable to reject the null hypothesis at 1% level of significance. Therefore we do not have enough evidence to support the claim that more than half of all those using the drug experienced relief.