Formulate the null and alternative hypotheses that can be used to suggest that the average earnings of this university’s work-study students were significantly higher than the national mean
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A: Population mean = ? = 907 Sample S.D = s =205 Sample size = n =500 Sample mean = x̅ = 825
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A: According to the given information in this question, we need to answer all the parts
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It is an important problem in testing of hypothesis . It has got wide applications in all types of inference problems .
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- Suppose Michigan State University's Collegiate Employment Institute found that starting salaries for recipients of bachelor's degrees in business was $50,032 in 2017. The results for a sample of 100 business majors receiving a bachelor's degree in 2018 showed a mean starting salary of $51,279 with a sample standard deviation of $5,200. Conduct a hypothesis test to determine whether the mean starting salary for business majors in 2018 is greater than the mean starting salary in 2017. Use ? = 0.01 as the level of significance. State the null and alternative hypotheses. (Enter != for ≠ as needed.) H0: Ha: Find the value of the test statistic. (Round your answer to three decimal places.) Find the p-value. (Round your answer to four decimal places.) p-value = State your conclusion. Reject H0. There is insufficient evidence to conclude that the mean starting salary for business majors has increased in 2018. Reject H0. There is sufficient evidence to conclude that…A new small business wants to know if its current radio advertising is effective. The owners decide to look at the mean number of customers who make a purchase in the store on days immediately following days when the radio ads are played as compared to the mean for those days following days when no radio advertisements are played. They found that for 1010 days following no advertisements, the mean was 18.618.6 purchasing customers with a standard deviation of 1.51.5 customers. On 77 days following advertising, the mean was 20.320.3 purchasing customers with a standard deviation of 0.90.9 customers. Test the claim, at the 0.020.02 level, that the mean number of customers who make a purchase in the store is lower for days following no advertising compared to days following advertising. Assume that both populations are approximately normal and that the population variances are equal. Let days following no advertisements be Population 1 and let days following advertising be Population 2.…A report about how American college students manage their finances includes data from a survey of college students. Each person in a representative sample of 793 college students was asked if they had one or more credit cards and if so, whether they paid their balance in full each month. There were 500 who paid in full each month. For this sample of 500 students, the sample mean credit card balance was reported to be $825. The sample standard deviation of the credit card balances for these 500 students was not reported, but for purposes of this exercise, suppose that it was $205. Is there convincing evidence that college students who pay their credit card balance in full each month have a mean balance that is lower than $907, the value reported for all college students with credit cards? Carry out a hypothesis test using a significance level of 0.01. State the appropriate null and alternative hypotheses. H0: ? = 907 Ha: ? < 907 H0: ? = 907 Ha: ? > 907 H0: ? < 907…
- Suppose the mean net worth of the resi- dents of Sun City, a retirement community, is $611,000 (Source: The Island Packet). If their net worth is nor- mally distributed with a standard deviation of $96,000,what percent of the residents have net worths between $700,000 and $800,000?The Chartered Financial Analyst (CFA) designation is fast becoming a requirement for serious investment professionals. It is an attractive alternative to getting an MBA for students wanting a career in investment. A student of finance is curious to know if a CFA designation is a more lucrative option than an MBA. He collects data on 38 recent CFAs with a mean salary of $138,000 and a standard deviation of $34,000. A sample of 80 MBAs results in a mean salary of $130,000 with a standard deviation of $46,000.a) Specify the hypotheses to test whether a CFA designation is more lucrative than an MBA.b) Calculate the value of the test statistic and the p-value. Do not assume that the population variances are equal.c) At the 5% significance level, is a CFA designation more lucrative than an MBA?The Chartered Financial Analyst (CFA) designation is fast becoming a requirement for serious investment professionals. It is an attractive alternative to getting an MBA for students wanting a career in investment. A student of finance is curious to know if a CFA designation is a more lucrative option than an MBA. He collects data on 36 recent CFAS with a mean salary of $145,000 and a standard deviation of $36,000. A sample of 47 MBAS results in a mean salary of $135,000 with a standard deviation of $24,000. Assume that H, is the population mean for individuals with a CFA designation and u, is the population mean of individuals with MBAS. (You may find it useful to reference the appropriate table: z table or t table) a. Set up the hypotheses to test if a CFA designation is more lucrative than an MBA at the 10% significance level. O Họ: 41- H2 = 0; HA: H1 - H2# 0 O Ho: 1-4220; HA H1 - 4200 b-1. Calculate the value of the test statistic. Do not assume that the population variances are…
- The mean work week for engineers in start-up companies is claimed to be about 59 hours with a standard deviation of 6 hours. Kara, a newly hired engineer hopes that it's not (she wants it to be shorter). She asks 10 engineers in start-ups for the lengths of their mean work weeks. Their responses are 70; 45; 55; 60; 65; 55; 55; 60; 50; 55.a. Is the newly hired engineer testing a mean or a proportion? mean proportion Correct b. The null hypothesis (or company claim), in symbols, is μ=μ=Correct.c. If the claim is correct, what is the probability that a sample mean would be as low as Kara's mean?Incorrect %Give your answer as a percentage accurate to one decimal place.According to Kaiser Family Foundation survey in 2011 and 2010, the average premium for employer-sponsored health insurance for family coverage was $15,073 in 2011 and $13,770 in 2010 (USA TODAY, September 29, 2011). Suppose that these averages were based on random samples of 250 and 200 employees who had such employer-sponsored health insurance plans for 2011 and 2010, respectively. Further assume that the population standard deviations for 2011 and 2010 were $2160 and $1990, respectively.According to the Insurance Association in US, the average annual expenditure for automobile insurance is $605. Suppose that in a simple random sample of 80 residents of New York, for most recent year their average expenditure was $638.62 with the standard deviation of $106.05. Based on these data, examine whether the average annual insurance for motorists in New York might be different from that in national level. Using the 0.05 level of significance, what conclusion do you reach? Also, construct and interpret 95% confidence interval for the population mean. Is the hypothesized mean within the interval? Is this consistent with the findings of the hypothesis test conducted?
- In a sample of 351 gamers between the ages of 16-25, the mean number of hours spent gaming per week was 42.5 hours. In a sample of 269 gamers between the ages of 26-40, the mean number of hours spent gaming per week was 43.8 hours. If the population standard deviation for the mean number of hours spent gaming per week is 9.5 for the age group 16-25 and 10.7 for the age group 26-40, test the claim that gamers between the ages of 16-25 spend less time gaming per week than gamers between the ages of 26-40. Assume α=0.03. Let population 1 be gamers in the age group 16-25 and population 2 be gamers in the age group 26-40. Round the test statistic to two decimal places, and round the p-value to four decimal places. The test statistic is . The p-value is . Should the null hypothesis be rejected?In one city, the average amount of time that tenth-graders spend watching television each week is 23 hours. The principal of Birchwood High School believes it is less for the 10th grade students that at his school. For a sample of 95 tenth-graders from the school, the mean amount of time spent watching television per week was 21.9 hours. Assuming a population standard deviation of 3.1 hours, does the data provide sufficient evidence to conclude that for all tenth-graders at Birchwood High school, the mean amount of time spent watching television per week is less than the city average of 23 hours? Perform the appropriate hypothesis test using a significance level of 0.005. What are the hypotheses? What is the test statistic? Is it a z or a t? Find the P-value for this test statistic. How does it compare to the significance level? On the normal curve, indicate the location of the test statistic and the p-value. (label them on the graph) Write…According to the Bureau of Labor Statistics, the mean salary for registered nurses in Kentucky was $55,130. The distribution of salaries is assumed to be normally distributed with a standard deviation of $5,778. Someone would like to determine if registered nurses in Ohio have a greater average pay. To investigate this claim, a sample of 220 registered nurses is selected from the Ohio Board of Nursing, and each is asked their annual salary. The mean salary for this sample of 220 nurses is found to be $55,504.488. Completely describe the sampling distribution of the sample mean salary when samples of size 220 are selected. mean: μ x-bar = ____ standard deviation: σ x-bar = ____ shape: the distribution of is ____________(not normally distributed/normally distributed) because ___________ (the sample size is large/the sample size is not large/the population of salaries is normally distributed/the population of salaries is not normally distributed)
