Question

In: Statistics and Probability

The manager of a Farmer John Super Market would like to know if there is a...

The manager of a Farmer John Super Market would like to know if there is a preference for the day of the week on which customers do their shopping. A sample of 420 families revealed the following. At he 0.05 significance level, is there a difference in the proportion of customers that prefer each day of the week?

Days of the week	Number of persons
Monday	20
Tuesday	30
Wednesday	20
Thursday	60
Friday	80
Saturday	130
Sunday	80

a. State the null and alternate hypothesis.

b. State the decision rule.

c. Compute the value of the test statistic.

Days of week
Monday
Tuesday
Wednesday
Thursday
Friday
Saturday
Sunday
Total

d. What is your decision regarding the null hypothesis? Interpret the result.

Expert Solution

The manager of a Farmer John Super Market would like to know if there is a preference for the day of the week on which customers do their shopping. A sample of 420 families revealed the following. At he 0.05 significance level, is there a difference in the proportion of customers that prefer each day of the week?

a. State the null and alternate hypothesis.

Ho: proportion of customers that prefer each day of the week is same

H1: proportion of customers that prefer each day of the week is different

b. State the decision rule.

Critical chi square with 6 df at 0.05 level =12.592

Rejection Rule: Reject Ho if calculated chi square > 12.592

c. Compute the value of the test statistic.

Goodness of Fit Test

	observed	expected	O - E	(O - E)² / E	% of chisq
	20	60.000	-40.000	26.667	16.33
	30	60.000	-30.000	15.000	9.18
	20	60.000	-40.000	26.667	16.33
	60	60.000	0.000	0.000	0.00
	80	60.000	20.000	6.667	4.08
	130	60.000	70.000	81.667	50.00
	80	60.000	20.000	6.667	4.08
Total	420	420.000	0.000	163.333	100.00

	163.333	chi-square
	6	df
	0.0000	p-value

d. What is your decision regarding the null hypothesis? Interpret the result.

calculated chi square = 163.33 which is > 12.592. we reject Ho.

We conclude that there is a difference in the proportion of customers that prefer each day of the week.

orchestra answered 1 year ago

In investing, we would like to know the overall trend of the market. Is the market...

In investing, we would like to know the overall trend of the market. Is the market trending up? Or, is it trending down? If the market is trending up, we want to be invested in stocks or Exchange Traded Funds (ETFs), such as DIA, SPY, QQQ, SSO, DDM, or QLD to name several. If the market is trending down, we really do not want to be in stocks, because we all know too well what happens to stock prices in...

The manager of a store would like to know if the average daily sales (measured in...

The manager of a store would like to know if the average daily sales (measured in dollars) through her website are any different than her in-store sales. The data has been collected on 51 days on website and in store. Perform an analysis at 5% significance level. Start by stating the hypothesis. Online In-Store 805.45 1400.76 780.27 969.27 927.79 1049.61 812.86 1453.6 550.91 876.72 901.07 1119.49 869.76 976.6 867.17 1017.76 801.91 482.12 973.15 1149.21 746.65 809.37 980.25 968.43 892.53 1077.45...

Student's t Distribution CI The manager of The Cheesecake Factory in Boston would like to know...

Student's t Distribution CI The manager of The Cheesecake Factory in Boston would like to know the mean number of customers served on weekdays. She believes that the number of customers served follows a Normal distribution. She reports that on six randomly selected weekdays an average of 158.3 customers were served with a sample standard deviation of 52.2. a. Calculate the standard error of the sample mean. b Find the t-critical value for a 99% confidence interval with a sample...

A bank manager would like the know the mean wait time for his customers. He randomly...

A bank manager would like the know the mean wait time for his customers. He randomly selects 25 customers and record the amount of time wait to see a teller. The sample mean is 7.25 minutes with a standard deviation of 1.1 minutes. Construct a 99% confidence interval for the mean wait time. Round your answers to 2 decimal places. Lower Limit = Upper Limit = Write a summary sentence for the confidence interval you calculated

A farmer wanted to know if the amount of feed consumed by his chickens would be...

A farmer wanted to know if the amount of feed consumed by his chickens would be affected by the presence or absence of hatchlings. Two groups of chickens were raised from hatching either singly or in a group of five hatch-mates. At the age of six weeks, all subjects were placed in a small cage with a same-aged, group-reared chicken (in the case of group-reared subjects, the test chicken was from a different group). The following data represents the amount...

I would just like to know if ANOVA would be the correct test to use for...

I would just like to know if ANOVA would be the correct test to use for the following problem below? Fancy Fish, a fine dining upscale restaurant in Northridge, California and 2016 Open Table Diners’ Choice award winner, is enjoying its eighteenth season of providing delectable food, exceptional service, and beautiful outdoor dining experiences. “Saturday - Half-off Bottled Wine Night” has made Fancy Fish one of the San Fernando Valley’s favorite restaurants. Every Saturday night, guests can enjoy half-off every...

A firm would like to know the proportion of it employees that expect to receive a...

A firm would like to know the proportion of it employees that expect to receive a raise within the next year the firm survey is 150 employees and finds that 60 expect to raise construct a 90% confidence interval for the population proportion a) what is the sample proportion b) State the critical value c) calculate the margin of error d) State the lower and upper values for the confidence interval

I would like to know the critical thinking portion of the questions

The marketing manager of a large super-market chain has the business objective of using shelf space...

The marketing manager of a large super-market chain has the business objective of using shelf space most efficiently. Toward that goal, they would like to use shelf space to predict the sales of a specialty pet food. Data are collected from a random sample of 12 equal-sized store, with the following results: Shelf Space Sales Aisle Location 5 160 0 5 220 1 5 140 0 10 190 0 10 240 0 10 260 1 15 230 0 15 270...

You would like to know whether there is a difference between the rate of cooling of...

You would like to know whether there is a difference between the rate of cooling of freshly killed corpses versus those that were reheated (to determine if you could fool a coroner about time of death). You tested several rats for their cooling constant, both when the rat was freshly killed and after the same rat was reheated. Assuming the distribution ofn differences is normal, is there any difference in the cooling constants between freshly killed and reheated rats? Test...