Question

Recently, research suggested that eating eggs is again considered potentially bad for your heart health. You are part of a team that did a healthy diet information talk to 50 students randomly chosen at the University of Arizona. After a year, you surveyed the same 50 people to find out if the average number of eggs eaten was significantly less than the US average of 1.7 per week. The sample mean was 1.5 eggs/week and sample standard deviation was 0.3 eggs/week.

1. State the question (ID the population)
2. State your null and alternative hypotheses (use population terms, define symbols)
3. Analyze your data statistically (set-up the equation and calculate a * value)
4. Assume the 1 tail critical value is 1.68. 2 tail critical value = 2.02    Do you reject or not reject the null hypothesis?
5.     Provide a statement of conclusion that includes the statistical evidence (3 pieces: * value, n, p-value either >0.05 or <0.05) and makes inference back to the population

Please tear off a small strip of paper and record your personal data anonymously. Write yes if you HAVE been to the dentist in the last 6 months, check no if you have NOT been to the dentist in the last 6 months. Use your discussion section’s sample percentage that have been to the dentist in the last months as a sample for the University of Arizona students go to the dentist at a significantly different percent than the US average of 55%.

ASSUME YOUR DATA ARE: DISCUSSION VALUE = 0.6 for a sample of size 28. You do not need a sample standard deviation because this is a question about a percent not a mean == see equation sheet State the question (ID the population)

1. State the question (ID the population)
2. State your null and alternative hypotheses (use population terms, define symbols)
3. Analyze your data statistically (set-up the equation and calculate a * value)
4.     Assume the 1 tail critical value is 1.65. 2 tail critical value = 1.96    Do you reject or not reject the null
5. hypothesis?
6. Provide a statement of conclusion that includes the statistical evidence (3 pieces: * value, n, p-value either >0.05 or <0.05)and makes inference back to the population.

3.     For each of the following, Identify the correct statistical test to use (choices are: 1 population z-test for mean, 1 population t-test for mean, 1 population z-test for percent), determine whether the question is left, right or both tailed questions.     Assume each meets assumptions of normality and that alpha is set at 0.05. The z* or t* value will always be calculated as:   (sample value – hypothesized value).

1.      60 out of 100 students at the U of MD prefer Pepsi to coke products. Is this significantly different than known 57% for the US population? Test: Is this a left right or both tailed question?
2.      For years, 80% of people going to a Nationals baseball game would purchase something to eat. This year you survey 100 people and find that only 75% planned to buy food. Has the percent of food purchasers decreased? Test:   Is this a left           right or both tailed question?
3. Should I buy gas in PG county? The average cost last week for gas in D.C. was $1.92. I surveyed 20 gas stations in PG county and found that the average cost was $1.86 with a sample standard deviation of $0.21. Is this a significant difference? Test:   Is this a left         right or both tailed question?
4.      Where have all the song birds gone? This year the average number of visitors to my bird feeder was 3.5 per day. Somehow I know the population standard deviation is 0.3.   Is this number a significant decrease from 5 years ago when the number was 4.1? Test: Is this a left         right or both tailed question?

Answer 1

Claim: To test whether that the average number of eggs eaten was significantly less than the US average of 1.7 per week or not

Hypothesis :

  

Left tailed test

Test statistics :

Where sample mean = 1.5

sample sd = s=0.3

sample size = n = 50

we get     

DF = n - 1 = 49

Critical value : tc = -1.677

Decision Rule : We Reject Ho

Conclusion : There is insufficient evidence to conclude that the average number of eggs eaten was less than the US average of 1.7 per week .