Free Printable Workshop: Hypothesis Testing

1.

Surveys'R'Us polled 209 adults in 2010 to see how many hours they spent on the internet per week. The sample mean was 6.75 hours with a standard deviation of 7.71. They took another sample of 541 adults in 2017 and found a sample mean of 7.34 hours and a standard deviation of 10.93. Perform a hypothesis test to determine if the population mean number of hours per week spent on the internet by adults has increased from 2010 to 2017. Use a 0.05 level of significance.

Choose the correct null and alternate hypothesis statements.

a)

$H_0:\ \ \mu_1\ne\mu_2\ \ \ \ \ \ \ \ \ \ \ H_1:\ \ \mu_1=\mu_2$

b)

$H_0:\ \ \mu_1>\mu_2\ \ \ \ \ \ \ \ \ \ \ H_1:\ \ \mu_1<\mu_2$

c)

$H_0:\ \ \mu_1=\mu_2\ \ \ \ \ \ \ \ \ \ \ H_1:\ \ \mu_1\ne\mu_2$

d)

$H_0:\ \ \mu_1=\mu_2\ \ \ \ \ \ \ \ \ \ \ H_1:\ \ \mu_1>\mu_2$

2.

Surveys'R'Us polled 209 adults in 2010 to see how many hours they spent on the internet per week. The sample mean was 6.75 hours with a standard deviation of 7.71. They took another sample of 541 adults in 2017 and found a sample mean of 7.34 hours and a standard deviation of 10.93. Perform a hypothesis test to determine if the population mean number of hours per week spent on the internet by adults has increased from 2010 to 2017. Use a 0.05 level of significance.

Choose the correct test to run.

a)

2 Samp Z Test

b)

2 Samp T Test

c)

2 Prop Z Test

d)

T Test

3.

Surveys'R'Us polled 209 adults in 2010 to see how many hours they spent on the internet per week. The sample mean was 6.75 hours with a standard deviation of 7.71. They took another sample of 541 adults in 2017 and found a sample mean of 7.34 hours and a standard deviation of 10.93. Perform a hypothesis test to determine if the population mean number of hours per week spent on the internet by adults has increased from 2010 to 2017. Use a 0.05 level of significance.

What is the p-value? Round to the fourth decimal place.

(a)

4.

Surveys'R'Us polled 209 adults in 2010 to see how many hours they spent on the internet per week. The sample mean was 6.75 hours with a standard deviation of 7.71. They took another sample of 541 adults in 2017 and found a sample mean of 7.34 hours and a standard deviation of 10.93. Perform a hypothesis test to determine if the population mean number of hours per week spent on the internet by adults has increased from 2010 to 2017. Use a 0.05 level of significance.

a)

Reject the Null

b)

Fail to Reject the Null

c)

Accept the Null

5.

Surveys'R'Us polled 209 adults in 2010 to see how many hours they spent on the internet per week. The sample mean was 6.75 hours with a standard deviation of 7.71. They took another sample of 541 adults in 2017 and found a sample mean of 7.34 hours and a standard deviation of 10.93. Perform a hypothesis test to determine if the population mean number of hours per week spent on the internet by adults has increased from 2010 to 2017. Use a 0.05 level of significance.

a)

There is enough evidence to conclude that population mean number of hours per week spent on the internet by adults has increased from 2010 to 2017.

b)

There is not enough evidence to conclude that population mean number of hours per week spent on the internet by adults has increased from 2010 to 2017.

c)

There is enough evidence to conclude that population mean number of hours per week spent on the internet by adults has decreased from 2010 to 2017.

d)

There is not enough evidence to conclude that population mean number of hours per week spent on the internet by adults has decreased from 2010 to 2017.

6.

Surveys'R'Us polled 209 adults in 2010 to see how many hours they spent on the internet per week. The sample mean was 6.75 hours with a standard deviation of 7.71. They took another sample of 541 adults in 2017 and found a sample mean of 7.34 hours and a standard deviation of 10.93. Perform a hypothesis test to determine if the population mean number of hours per week spent on the internet by adults has increased from 2010 to 2017.

Calculate the 90% confidence interval to estimate the difference in the means from 2010 and 2017. Enter the confidence interval in parenthesis, separated by a comma. Round to the 3rd decimal place. (NO SPACES!!!)

(a)

7.

In 2005, 5000 children under 10 were surveyed and it was found that 595 of them had cell phones. In 2009, another 5000 children were sampled and it was found that 1000 of them had cell phones.

Construct a 95% confidence interval for the difference in the proportion of children under 10 with cell phones between 2005 and 2008. Enter the confidence interval in parenthesis, separated by a comma. Round to the fourth decimal place. (NO SPACES)!

(a)

8.

In a clinical trial, two pain reliever drugs were tested. A sample of 100 patients were given Drug A. A second sample of 200 patients were given Drug B. 76 of the patients given drug A experienced substantial pain relief. 128 of the patients given drug B experience substantial pain relief. Perform a hypothesis test at the 0.05 significance level to determine if the proportion of patients experiencing substantial relief is greater for drug A.

State the null and alternate hypothesis statements.

a)

$H_0:\ \ P_A>P_B\ \ \ \ \ \ \ \ \ \ \ H_1:\ \ P_A<P_B$

b)

$H_0:\ \ P_A\ne P_B\ \ \ \ \ \ \ \ \ \ \ H_1:\ \ P_A=P_B$

c)

$H_0:\ \ P_A\ =P_B\ \ \ \ \ \ \ \ \ \ \ H_1:\ \ P_A\ >P_B$

d)

$H_0:\ \ P_A\ <P_B\ \ \ \ \ \ \ \ \ \ \ H_1:\ \ P_A\ >P_B$

9.

In a clinical trial, two pain reliever drugs were tested. A sample of 100 patients were given Drug A. A second sample of 200 patients were given Drug B. 76 of the patients given drug A experienced substantial pain relief. 128 of the patients given drug B experience substantial pain relief. Perform a hypothesis test at the 0.05 significance level to determine if the proportion of patients experiencing substantial relief is greater for drug A.

What type of test should you run?

a)

Z Test

b)

1 Prop Z Test

c)

2 Sample T Test

d)

2 Prop Z Test

10.

In a clinical trial, two pain reliever drugs were tested. A sample of 100 patients were given Drug A. A second sample of 200 patients were given Drug B. 76 of the patients given drug A experienced substantial pain relief. 128 of the patients given drug B experience substantial pain relief. Perform a hypothesis test at the 0.05 significance level to determine if the proportion of patients experiencing substantial relief is greater for drug A.

What is the p-value? Round to the fourth decimal place.

(a)

11.

In a clinical trial, two pain reliever drugs were tested. A sample of 100 patients were given Drug A. A second sample of 200 patients were given Drug B. 76 of the patients given drug A experienced substantial pain relief. 128 of the patients given drug B experience substantial pain relief. Perform a hypothesis test at the 0.05 significance level to determine if the proportion of patients experiencing substantial relief is greater for drug A.

Choose the correct decision.

a)

Reject the Null

b)

Fail to Reject the Null

c)

Accept the Null

12.

In a clinical trial, two pain reliever drugs were tested. A sample of 100 patients were given Drug A. A second sample of 200 patients were given Drug B. 76 of the patients given drug A experienced substantial pain relief. 128 of the patients given drug B experience substantial pain relief. Perform a hypothesis test at the 0.05 significance level to determine if the proportion of patients experiencing substantial relief is greater for drug A.

Choose the correct decision.

a)

There is enough evidence to conclude that the proportion of patients experiencing substantial relief is greater for drug A.

b)

There is not enough evidence to conclude that the proportion of patients experiencing substantial relief is greater for drug A.

c)

There is enough evidence to conclude that the proportion of patients experiencing substantial relief is less for drug A.

d)

There is not enough evidence to conclude that the proportion of patients experiencing substantial relief is less for drug A.

13.

Two fertilizers were tested in a study to determine the effects of each on the production of a certain fruit. Fertilizer A was used to treat 16 randomly selected plots of land. Fertilizer B was used to treat 12 randomly selected plots of land. The number of pounds of fruit harvested from each plot was determined and is listed below.

Fertilizer A: 445, 523, 464, 483, 441, 491, 403, 466, 448, 457, 437, 516, 417, 420, 400, 506

Fertilizer B: 362, 414, 408, 398, 382, 368, 393, 437, 387, 373, 424, 384

Assume that each population is approximately normal.

Construct a 98% confidence interval for the difference between the mean yields for the two types of fertilizer. Enter the confidence interval in parenthesis and separated by a comma, NO SPACES, rounded to 1 decimal place.

(a)

Workshop: Hypothesis Testing - 2 Samples (independent)

Total questions: 13

Worksheet time: 1hrs 5mins

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