Question

1. Given that the 90% confidence interval for the mean is from –0.34 to 7.28, how many integers would not be rejected as plausible values for the population mean for a two-tailed hypothesis test at a 10% significance level? _____integers would not be rejected.

2. Use a sample of 15 games each to see if your average score at Wii tennis is significantly greater than your friend’s average score.

Describe what it means in that context to make a Type I and Type II error.

• A : Type I error: Find your average Wii tennis score is lower than a friend’s, when actually it isn’t.

  Type II error: The sample does not contain enough evidence to conclude that your average Wii tennis score is better than your friend’s mean, when actually it is better.

• B : Type I error: Find your average Wii tennis score is higher than a friend’s, when actually it isn’t.

  Type II error: The sample does not contain enough evidence to conclude that your average Wii tennis score is worse than your friend’s mean, when actually it is lower.

• C : Type I error: Find your average Wii tennis score is higher than a friend’s, when actually it isn’t.

  Type II error: The sample does not contain enough evidence to conclude that your average Wii tennis score is better than your friend’s mean, when actually it is better.

• D : Type I error: Find your average Wii tennis score is lower than a friend’s, when actually it isn’t.

  Type II error: The sample does not contain enough evidence to conclude that your average Wii tennis score is worse than your friend’s mean, when actually it is lower.

• E :None of the above.

• Q 3. In a study of a mean age of people buying a second car, the null hypothesis is that the mean age is 50 years. The alternative hypothesis is that the age is below 50 years. There are three samples, A, B, and C, representing mean ages of 28, 34, and 40 years with the p-values 0.02, 0.09 and 0.15, respectively. If the significance level is 10%, what can we say about the strength of the evidence these samples provide in support of the alternative hypothesis?

• A : Samples A and B give strong evidence in support of the alternative hypothesis, while sample C gives little evidence.

• B : Samples A and B give very strong evidence in support of the alternative hypothesis, while sample C gives moderate evidence.

• C : Sample A gives very strong evidence in support of the alternative hypothesis, sample B gives strong evidence and sample C gives moderate evidence.

• D : Sample A gives strong evidence in support of the alternative hypothesis, sample B gives moderate evidence and sample C gives little evidence.

• E :Sample A gives strong evidence in support of the alternative hypothesis, while samples B and C gives little evidence.

Q 4. A hypothesis test explores, if people with Ph. D., on average, search for a new job longer than 60 days after leaving the previous one. The first sample has the sample mean of 75 days and gives the p-value of 0.017, which indicates that we have the evidence in support of the claim. The second test provides even stronger evidence in support of the claim. What can we say about the sample mean and the p-value of the second sample?

• A : The sample mean of the second sample is greater than 75 days. The p-value is less than 0.017.

• B : The sample mean of the second sample is less than 75 days. The p-value is less than 0.017.

• C : The sample mean of the second sample is 75 days. The p-value is less than 0.017.

• D : The sample mean of the second sample is greater than 75 days. The p-value is greater than 0.017.

• E : The sample mean of the second sample is less than 75 days. The p-value is greater than 0.017.

Q 5. A sociological research revealed, that out of 10,000 respondents, 2500 prefer to read books in the paper format, 3500 use mostly digital format, 1000 use both formats, and 3000 do not read books systematically. If the null hypothesis is that the proportion of people who use both formats is equal to 0.25 and the alternative hypothesis is that the proportion of people who use both formats is less than 0.25, what can we say about the conclusion of the hypothesis test?

• A : We reject the null hypothesis and support the alternative hypothesis, so the proportion of people who use both formats is equal to 0.25.

• B : We reject the null hypothesis and support the alternative hypothesis, so the proportion of people who use both formats is less than 0.25.

• C : The data in the research are insufficient to state the conclusion to the hypothesis test.

• D :We do not reject the null hypothesis, so the proportion of people who use both formats is less than 0.25.

• E :We do not reject the null hypothesis, so the proportion of people who use both formats is equal to 0.25.

Answer 1

Solution: Here concept of hypothesis testing is used.

Solution i- - We would not reject the null hypothesis is the I value of the mean under the null hypothesis lies in the confidence interval. Between the given interval & integers lie (0, 1, 2, 3, 4, 5, 6 and 7). Hence, we would not reject there 8 - integers. - 8 integers would not be rejected. - 2) Type I error: The error commited by rejecting the noll hypothesis when it is true. Type I error: The error commited by not rejecting E the null hypothesis when it is false. Type I error and Type II error for the given context as follows: I - - Type I error! Find your average ware wil tennis score is higher than a friend's when actually it isn't. Type II error: The sample does not contain enough. evidence to conclude that your average Wii tennis score is better than your friend's mean, when actually it is better. Hence, the option (c) is correct.