Homework

The mean number of English courses taken in a two–year time period by men and women college students is believed to be about the same. An experiment is conducted and data are collected from 29 men and 16 women. The men took an average of three English courses with a standard deviation of 0.8. The women took an average of four English courses with a standard deviation of 1.0. Are the means statistically the same?

At Rachel’s 11^th birthday party, eight guests were timed to see how long (in seconds) they could hold their breath in a relaxed position. After a two-minute rest, they timed themselves while jumping. The children thought that the mean difference between their jumping and relaxed times would be zero. Test their hypothesis.

Marketing companies have collected data implying that teenage girls use more social media apps on their smartphones than teenage boys do. In one particular study of 40 randomly chosen teenage girls and boys (20 of each) with smartphones, the mean number of social media apps for the girls was 3.2 with a standard deviation of 1.5. The mean for the boys was 1.7 with a standard deviation of 0.8. Conduct a hypothesis test to determine if the means are approximately the same or if the girls’ mean is higher than the boys’ mean.

Repeat the test in Exercise 10.69, but use Lap 5 data this time.

In two to three complete sentences, explain in detail how you might use Terri Vogel’s data to answer the following question. “Does Terri Vogel drive faster in races than she does in practices?”

The exact distribution for the hypothesis test is:

1. the normal distribution
2. the Student's t-distribution
3. the uniform distribution
4. the exponential distribution

Suppose a statistics instructor believes that there is no significant difference between the mean class scores of statistics day students on Exam 2 and statistics night students on Exam 2. They take random samples from each of the populations. The mean and standard deviation for 35 statistics day students were 75.86 and 16.91. The mean and standard deviation for 37 statistics night students were 75.41 and 19.73. The “day” subscript refers to the statistics day students. The “night” subscript refers to the statistics night students. A concluding statement is:

1. There is sufficient evidence to conclude that statistics night students' mean on Exam 2 is better than the statistics day students' mean on Exam 2.
2. There is insufficient evidence to conclude that the statistics day students' mean on Exam 2 is better than the statistics night students' mean on Exam 2.
3. There is insufficient evidence to conclude that there is a significant difference between the means of the statistics day students and night students on Exam 2.
4. There is sufficient evidence to conclude that there is a significant difference between the means of the statistics day students and night students on Exam 2.

A powder diet is tested on 49 people, and a liquid diet is tested on 36 different people. Of interest is whether the liquid diet yields a higher mean weight loss than the powder diet. The powder diet group had a mean weight loss of 42 pounds with a standard deviation of 12 pounds. The liquid diet group had a mean weight loss of 45 pounds with a standard deviation of 14 pounds.

A recent drug survey showed an increase in the use of drugs and alcohol among local high school seniors as compared to the national percent. Suppose that a survey of 100 local seniors and 100 national seniors is conducted to see if the proportion of drug and alcohol use is higher locally than nationally. Locally, 65 seniors reported using drugs or alcohol within the past month, while 60 national seniors reported using them.

Elizabeth Mjelde, an art history professor, was interested in whether the value from the Golden Ratio formula, $\left(\frac{\text{larger + smaller dimension}}{\text{larger dimension}}\right)$ was the same in the Whitney Exhibit for works from 1900 to 1919 as for works from 1920 to 1942. Thirty-seven early works were sampled, averaging 1.74 with a standard deviation of 0.11. Sixty-five of the later works were sampled, averaging 1.746 with a standard deviation of 0.1064. Do you think that there is a significant difference in the Golden Ratio calculation?

This is:

1. a test of two proportions
2. a test of two independent means
3. a test of a single mean
4. a test of matched pairs

Adults aged 18 years old and older from a certain city were randomly selected for a survey on working from home. The researchers wanted to determine if the proportion of women who work from home is less than the proportion of men who work from home. The results are shown in Table 10.24. Test at the 1% level of significance.

A group of friends debated whether more people in their twenties use wearable fitness devices than people in their thirties. They consulted a research study of wearable fitness device use among adults. The results of the survey indicate that of the 973 randomly sampled people in their twenties, 379 use such devices. For people in their thirties, 404 of the 1,304 who were randomly sampled use wearable fitness devices. Test at the 5% level of significance.

We are interested in whether children’s educational computer software costs less, on average, than children’s entertainment software. Thirty-six educational software titles were randomly picked from a catalog. The mean cost was $31.14 with a standard deviation of $4.69. Thirty-five entertainment software titles were randomly picked from the same catalog. The mean cost was $33.86 with a standard deviation of $10.87. Decide whether children’s educational software costs less, on average, than children’s entertainment software.

A study is done to determine if students in the California state university system take longer to graduate, on average, than students enrolled in private universities. One hundred students from both the California state university system and private universities are surveyed. Suppose that from years of research, it is known that the population standard deviations are 1.5811 years and 1 year, respectively. The following data are collected. The California state university system students took on average 4.5 years with a standard deviation of 0.8. The private university students took on average 4.1 years with a standard deviation of 0.3.

A group of transfer bound students wondered if they will spend the same mean amount on texts and supplies each year at their four-year university as they have at their community college. They conducted a random survey of 54 students at their community college and 66 students at their local four-year university. The sample means were $947 and $1,011, respectively. The population standard deviations are known to be $254 and $87, respectively. Conduct a hypothesis test to determine if the means are statistically the same.

A baseball fan wanted to know if there is a difference between the number of games played in a World Series when the American League won the series versus when the National League won the series. From 1922 to 2012, the population standard deviation of games won by the American League was 1.14, and the population standard deviation of games won by the National League was 1.11. Of 19 randomly selected World Series games won by the American League, the mean number of games won was 5.76. The mean number of 17 randomly selected games won by the National League was 5.42. Conduct a hypothesis test.

A new heart disease prevention drug was tried on a group of 224 patients. Forty-five patients developed heart disease after four years. In a control group of 224 patients, 68 developed heart disease after four years. We want to test whether the method of treatment reduces the proportion of patients that develop heart disease after four years or if the proportions of the treated group and the untreated group stay the same.

Let the subscript t = treated patient and ut = untreated patient.

The appropriate hypotheses are:

1. H₀: p_t < p_ut and H_a: p_t ≥ p_ut
2. H₀: p_t ≤ p_ut and H_a: p_t > p_ut
3. H₀: p_t = p_ut and H_a: p_t ≠ p_ut
4. H₀: p_t = p_ut and H_a: p_t < p_ut

An experiment is conducted to show that blood pressure can be consciously reduced in people trained in a “biofeedback exercise program.” Six subjects were randomly selected and blood pressure measurements were recorded before and after the training. The difference between blood pressures was calculated (after - before) producing the following results: ${\bar{x}}_d$ = −10.2 s_d = 8.4. Using the data, test the hypothesis that the blood pressure has decreased after the training.

The distribution for the test is:

1. t₅
2. t₆
3. N(−10.2, 8.4)
4. N(−10.2, $\frac{8.4}{\sqrt{6}}$)

A golf instructor is interested in determining if their new technique for improving players’ golf scores is effective. The instructor takes four new students and records their 18-hole scores before learning the technique and then after having taken the class. The instructor conducts a hypothesis test. The data are as follows.

The correct decision is:

1. Reject H₀.
2. Do not reject the H₀.

A traveler wanted to know if the prices of hotels are different in the ten cities that he visits the most often. The list of the cities with the corresponding hotel prices for his two favorite hotel chains is in Table 10.31. Test at the 1% level of significance.