A candidate for mayor wants to gauge potential voter reaction to an increase recreational services by estimating the proportion of voter who now use city services. If we assume that 50% of the voters require city recreational services, what is the probability that 40% or fewer voters in a sample of 100 actually will use these city services? First, let's do a test on the proportion using our [URL='http://www.mathcelebrity.com/proportion_hypothesis.php?x=+40&n=+100&ptype=%3D&p=+0.5&alpha=+0.05&pl=Proportion+Hypothesis+Testing']proportion hypothesis calculator[/URL]: We get Z = -2 Now use the [URL='http://www.mathcelebrity.com/zscore.php?z=p%28z%3C-2%29&pl=Calculate+Probability']z-score calculator[/URL] to get P(z<-2) = [B]0.02275[/B]

A firm wants to know with a 98% level of confidence if it can claim that the boxes of detergent it sells contain more than 500g of detergent. From past experience the firm knows that the amount of detergent in the boxes is normally distributed. The firm takes a random sample of n =25 and finds that X = 520 g and s = 75g. What's your final conclusion? (Ho: u = 500; Ha: u > 500) [URL='http://www.mathcelebrity.com/mean_hypothesis.php?xbar=520&n=25&stdev=75&ptype==&mean=500&alpha=0.02&pl=Mean+Hypothesis+Testing']Perform a hypothesis testing of the mean[/URL] [B]Yes, accept null hypothesis[/B]

A Government antipollution spokeperson asserts that more than 80% of the plants in the Glassboro area meet the antipollution standards. An antipollution advocate does not believe the government claim. She takes a random sample of published data on pollution emission for 64 plants in the area and finds that 56 plants meet the pollution standards. Do the sample data support the government claim at the 1% level of significance? (H0: ρ=0.8; H_a: ρ>0.8) [URL='http://www.mathcelebrity.com/proportion_hypothesis.php?x=+56&n=64&ptype==&p=+0.8&alpha=+0.01&pl=Proportion+Hypothesis+Testing']Perform a hypothesis testing of a proportion[/URL] [B]Accept null hypothesis[/B]

A researcher believed that there was a difference in the amount of time boys and girls at 7th grade studied by using a two-tailed t test. Which of the following is the null hypothesis? a. Mean of hours that boys studied per day was equal to mean of hours that girls studied per day b. Mean of hours that boys studied per day was greater than mean of hours that girls studied per day c. Mean of hours that boys studied per day was smaller than mean of hours that girls studied per day d. Mean of hours that boys studied per day was smaller than or equal to mean of hours that girls studied per day [B]a. Mean of hours that boys studied per day was equal to mean of hours that girls studied per day[/B] Reason is that in hypothesis testing, you take a position other than what is assumed or what is being tested as the null hypothesis

Free Confidence Interval/Hypothesis Testing for the Difference of Means Calculator - Given two large or two small distriutions, this will determine a (90-99)% estimation of confidence interval for the difference of means for small or large sample populations.
Also performs hypothesis testing including standard error calculation.

Conventionally, the null hypothesis is false if the probability value is: a. Greater than 0.05 b. Less than 0.05 c. Greater than 0.95 d. Less than 0.95 [B]b. Less than 0.05[/B] This is standard in hypothesis testing using p = 0.05

[URL]http://www.mathcelebrity.com/mean_hypothesis.php?xbar=469&n=40&stdev=73&ptype=%3D&mean=475&alpha=0.10&pl=Mean+Hypothesis+Testing[/URL]

[URL]http://www.mathcelebrity.com/mean_hypothesis.php?xbar=3.7&n=3.2&stdev=1.8&ptype=%3D&mean=4.2&alpha=0.05&pl=Mean+Hypothesis+Testing[/URL]

[URL]http://www.mathcelebrity.com/mean_hypothesis.php?xbar=20.5&n=11&stdev=7&ptype=%3D&mean=18.7&alpha=0.01&pl=Mean+Hypothesis+Testing[/URL]

Free Hypothesis Testing for a proportion Calculator - Performs hypothesis testing using a test statistic for a proportion value.

Free Hypothesis testing for the mean Calculator - Performs hypothesis testing on the mean both one-tailed and two-tailed and derives a rejection region and conclusion

Imagine that a researcher wanted to know the average weight of 5th grade boys in a high school. He randomly sampled 5 boys from that high school. Their weights were: 120 lbs., 99 lbs, 101 lbs, 87 lbs, 140 lbs. The researcher posed a null hypothesis that the average weight for boys in that high school should be 100 lbs. What is the [B][U]absolute value[/U][/B] of calculated t that we use for testing the null hypothesis? Mean is 109.4 and Standard Deviation = 20.79182532 using our [URL='http://www.mathcelebrity.com/statbasic.php?num1=120%2C99%2C101%2C87%2C140&num2=+0.2%2C0.4%2C0.6%2C0.8%2C0.9&pl=Number+Set+Basics']statistics calculator[/URL] Now use those values and calculate the t-value Abs(t value) = (100 - 109.4)/ 20.79182532/sqrt(5) Abs(tvalue) = [B]1.010928029[/B]

Free Random Sampling from the Normal Distribution Calculator - This performs hypothesis testing on a sample mean with critical value on a sample mean or calculates a probability that Z <= z or Z >= z using a random sample from a normal distribution.

Suppose a firm producing light bulbs wants to know if it can claim that its light bulbs it produces last 1,000 burning hours (u). To do this, the firm takes a random sample of 100 bulbs and find its average life time (X=980 hrs) and the sample standard deviation s = 80 hrs. If the firm wants to conduct the test at the 1% of significance, what's you final suggestion? (i..e, Should the producer accept the Ho that its light bulbs have a 1,000 burning hrs. at the 1% level of significance?) Ho: u = 1,000 hours. Ha: u <> 1,000 hours. [URL='http://www.mathcelebrity.com/mean_hypothesis.php?xbar=+980&n=+100&stdev=+80&ptype==&mean=+1000&alpha=+0.01&pl=Mean+Hypothesis+Testing']Perform a hypothesis test of the mean[/URL] [B]Yes, accept null hypothesis[/B]

Suppose that the manager of the Commerce Bank at Glassboro determines that 40% of all depositors have a multiple accounts at the bank. If you, as a branch manager, select a random sample of 200 depositors, what is the probability that the sample proportion of depositors with multiple accounts is between 35% and 50%? [URL='http://www.mathcelebrity.com/proportion_hypothesis.php?x=50&n=+100&ptype==&p=+0.4&alpha=+0.05&pl=Proportion+Hypothesis+Testing']50% proportion probability[/URL]: z = 2.04124145232 [URL='http://www.mathcelebrity.com/proportion_hypothesis.php?x=+35&n=+100&ptype==&p=+0.4&alpha=+0.05&pl=Proportion+Hypothesis+Testing']35% proportion probability[/URL]: z = -1.02062072616 Now use the [URL='http://www.mathcelebrity.com/zscore.php?z=p%28-1.02062072616

The margarita is one of the most common tequila-based cocktails, made with tequila, triple sec, and lime juice, often served with salt on the glass rim. A manager at a local bar is concerned that the bartender is not using the correct amounts of the three ingredients in more than 50% of margaritas. He secretly observed the bartender and found that he used the CORRECT amounts in only 9 out of the 39 margaritas in the sample. Use the critical value approach to test if the manager's suspicion is justified at ? = 0.10. Let p represent the proportion of all margaritas made by the bartender that have INCORRECT amounts of the three ingredients. Use Table 1. a. Select the null and the alternative hypotheses. [B]H0: p ? 0.50; HA: p > 0.50[/B] [B][/B] b. Calculate the sample proportion. (Round your answer to 3 decimal places.) 9/39 = [B]0.231 [/B] c. Calculate the value of test statistic. (Round your intermediate calculations to 4 decimal places and final answer to 2 decimal places.) Using our [URL='http://www.mathcelebrity.com/proportion_hypothesis.php?x=9&n=39&ptype=%3C&p=+0.5&alpha=+0.10&pl=Proportion+Hypothesis+Testing']proportion hypothesis calculator[/URL], we get: [B]Test Stat = -3.36[/B] [B][/B] d. Calculate the critical value. (Round your answer to 2 decimal places.) Using the link above, we get a critical value of [B]1.2816 [/B] e. What is the conclusion? [B]The manager’s suspicion is not justified since the value of the test statistic does not fall in the rejection region. Do not reject H0[/B] [B][/B]

True or False (a) The normal distribution curve is always symmetric to its mean. (b) If the variance from a data set is zero, then all the observations in this data set are identical. (c) P(A AND A^c)=1, where A^c is the complement of A. (d) In a hypothesis testing, if the p-value is less than the significance level ?, we do not have sufficient evidence to reject the null hypothesis. (e) The volume of milk in a jug of milk is 128 oz. The value 128 is from a discrete data set. [B](a) True, it's a bell curve symmetric about the mean (b) True, variance measures how far a set of numbers is spread out. A variance of zero indicates that all the values are identical (c) True. P(A) is the probability of an event and P(Ac) is the complement of the event, or any event that is not A. So either A happens or it does not. It covers all possible events in a sample space. (d) False, we have sufficient evidence to reject H0. (e) False. Volume can be a decimal or fractional. There are multiple values between 127 and 128. So it's continuous.[/B]

When you conduct a hypothesis testing, at which of the following P-value, you feel more confident to reject the null hypothesis? a. 0.05 b. 0.01 c. 0.95 d. 0.03 [B]b. 0.01[/B] [I]The lower the p value, the more confident you are about rejecting the null hypothesis.[/I]

Which of the following descriptions of null hypothesis are correct? (Select all that apply) a. A null hypothesis is a hypothesis tested in significance testing. b. The parameter of a null hypothesis is commonly 0. c. The aim of all research is to prove the null hypothesis is true d. Researchers can reject the null hypothesis if the P-value is above 0.05 [B]a. A null hypothesis is a hypothesis tested in significance testing. [/B] [I]b. is false because a parameter can be anything we choose it to be c. is false because our aim is to disprove or fail to reject the null hypothesis d. is false since a p-value [U]below[/U] 0.05 is often the rejection level.[/I]