statistics

posted by .

suppose you are testing Ho:p=.65 versus Ha: p<.65 . for a random sample of 100 people, x=58, where x denotes the number in the sample that have the characteristic of interest . use a .01 level of significance to test this hypothesis.

• statistics -

Null hypothesis:
Ho: p = .65 -->meaning: population proportion is equal to .65
Alternative hypothesis:
Ha: p < .65 -->meaning: population proportion is less than .65

Using a formula for a binomial proportion one-sample z-test with your data included, we have:

z = (.58 - .65) -->test value (58/100 = .58) minus population value (.65)
divided by
√[(.65)(.35)/100] --> .35 represents 1 - .65 and 100 is the sample size.

Use a z-table to find the critical or cutoff value for a one-tailed test (lower tail) at .01 level of significance. The test is one-tailed because the alternative hypothesis is showing a specific direction (less than).

If the test statistic exceeds the critical value you find from the table, reject the null. If the test statistic does not exceed the critical value from the table, do not reject the null.

You can draw your conclusions from there.

I hope this will help get you started.

Similar Questions

For the following independent random samples, use the z-test and the 0.01 level of significance in testing as an approximation to the unequal variances t-test when comparing two sample means?
2. statistics

A random sample of n = 30 is drawn from a population that is normally distributed, and the sample variance is s©÷ = 41.5. Use ¥á = 0.05 in testing ¥Ç₀ : ¥ò©÷ = 29.0 versus ¥Ç©û : ¥ò©÷ ¡Á 29.0
3. statistics

A random sample of n= 12 is drawn from a population that is normally distributed, and the sample variance is s©÷ = 19.3. Use ¥á = 0.025 in testing ¥Ç₀ : ¥ò©÷ ¡ 9.4 versus ¥Ç©û : ¥ò©÷ > 9.4
4. MTH233/statistics UOP

. Hypothesis Testing o Please complete the following 5-step hypothesis testing procedure in your Learning Teams: A simple random sample of forty 20-oz bottles of Coke® from a normal distribution is obtained and each bottle is measured …
5. Probability and Statistics

A research psychologist believes that professional athletes tend to be more confident than the typical person. From previous testing, he knows that the scores for people in the general population are approximately normally distributed …
6. sssc

Suppose we test H0 : p = .3 versus Ha : p ≠ .3 and that a random sample of n = 100 gives a sample proportion p = .20. a: Test H0 versus Ha at the .01 level of significance by using critical values. What do you conclude?
7. Statistics

2. In 2009 a random sample of 70 unemployed people in Alabama showed an average weekly benefit of \$199.65. In Mississippi, for a random sample of 65 the number was \$187.93. Assume population standard deviations of \$32.48 and \$26.15 …
8. statistics

A specific study found that the average number of doctor visits per year for people over 55 is 8 with a standard deviation of 2. Assume that the variable is normally distributed. 1. Identify the population mean. 2. Identify the population …
9. statistics

4. The Pew Research Center reported that 57% of Americans favored the Wall Street bailout of 2008. A random sample of 300 people showed that 155 people favored the bailout. If appropriate, test whether the population proportion of …
10. statistics

A management consultant has analysed a random sample of 40 large firms in order to investigate the mean annual salary of sales managers. She has constructed the following 90% confidence interval for the population mean annual salary: …

More Similar Questions