A company decided to test the hypothesis that the average time a company’s employees are spending to check their private e-mails at work is more than 9 minutes. A random sample of 50 employees were selected and they averaged 9.6 minutes. It is believed that the population standard deviation is 2.5 minutes. The α is set to 0.05. The p-value for this hypothesis test would be __________.
Question
A company decided to test the hypothesis that the average time a company’s employees are spending to check their private e-mails at work is more than 9 minutes. A random sample of 50 employees were selected and they averaged 9.6 minutes. It is believed that the population standard deviation is 2.5 minutes. The α is set to 0.05. The p-value for this hypothesis test would be __________.
Solution
To find the p-value for this hypothesis test, we first need to calculate the test statistic. This is a one-sample z-test because we have a sample mean, a population standard deviation, and we're testing a hypothesis about the population mean.
Step 1: State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: μ = 9 Alternative hypothesis: μ > 9
Step 2: Formulate an analysis plan. For this analysis, the significance level is defined as α = 0.05. We are to use a one-sample z-test to test the hypothesis.
Step 3: Analyze sample data. Using sample data, we calculate the pooled sample mean (x̄) and the standard error (SE). Using those measures, we compute the z-score (z).
x̄ = 9.6 μ = 9 σ = 2.5 n = 50
z = (x̄ - μ) / (σ/√n) = (9.6 - 9) / (2.5/√50) = 1.7
Step 4: Interpret the results. We use the Normal Distribution Calculator to find the probability that a z-score is less than 1.7. This probability corresponds to the p-value.
The p-value is 0.0446.
So, the p-value for this hypothesis test would be 0.0446.
Similar Questions
The manager of a grocery store has taken a random sample of 100 customers to determine whether or not the mean waiting time of all customers is significantly more than 3 minutes. She observes that the average length of time it took the customers in the sample to check out was 3.1 minutes. The population standard deviation is known to be 0.5 minutes.
A study conducted by a technology company showed that the mean time spent per day browsing the video streaming service Netflix for something to watch was 20.6 minutes. Assume the standard deviation is =σ8. Suppose a simple random sample of 102 visits taken this year has a sample mean of =x19.6 minutes. A social scientist is interested to know whether the mean time browsing Netflix has decreased. Use the =α0.05 level of significance and the P-value method with the TI-84 Plus calculator.Part: 0 / 50 of 5 Parts CompletePart 1 of 5(a) State the appropriate null and alternate hypotheses.H0: 20.6H1: 20.6
The waiting time to check out of a supermarket has had a population mean of 8.49 minutes.Recently,in an effort to reduce the waiting time,the supermarket has experimented with a system in which there is a single waiting line with multiple checkout servers.A sample of 90 customers was selected,and their mean waiting time to check out was 7.85 minutes with a sample standard deviation of 4.9 minutes.Complete parts(a)through(d) H0:μ≥8.49 H1:μ<8.49 What is the test statistic for this test? -1.2391 (Round to four decimal places as needed.) What is the critical value for this test?
The manager of a computer shop is recording the time taken for customers to decide of which computer and accessories they buy from the time they enter the store. From the previous data, it is known that the average ‘decision’ time was 45 minutes. The manager assumes a normally distributed population with a standard deviation of 10 minutesa) What is the probability that a customer will take more than 60 minutes?
The Sydney Airport Commission set a performance target of 24 minutes for the time taken for passengers to claim their luggage at domestic terminals. In order to monitor performance, a study was conducted by taking a random sample of 200 passengers disembarking from Sydney airport. If the study found a p-value of 0.5 what was the sample mean time taken by passengers to claim their luggage? (Your answer should be correct to one decimal place.)
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.