Ralph Henderson owns a cafe near MIT. His cafe is always crowded with students who need...

  
 
 
 
 
 
 
 

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Ralph Henderson owns a cafe near MIT. His cafe is always crowded with students who need caffeine to start their day. Ralph Henderson wants to serve the freshest coffee to his customers. He would like to understand his coffee sales better in order to roast the right amount of coffee beans every day. First, Ralph Henderson would like to explore the demand for pour-over coffee. He expects the daily demand for pour-over coffee to be stable at 130 cups per day. To test his hypothesis, he collected actual demand data for pour-over coffee for a week (see Table 1). Table 1. Actual demand and expected demand for pour-over coffee (in cups). actual demand expected demand 130 130 130 Monday 124 Tuesday 156 Wednesday 162 Thursday 129 nday 120 130 130 Run a chi-square test to compare actual and expected demand distributions. What is the p-value of your chi-square test? Round to FOUR decimal points Can Ralph state that the demand for pour-over coffee is significantly different from his expected distribution at 95% confidence? Choose the best answer The demand is significantly different from the expected distribution The demand is not significantly different from the expected distribution None of the above Ralph Henderson recently changed the price of a cup of latte. He would like to understand the latte sales better after the price change. Firstly, he decided to find out the confidence interval for daily latte sales after the price change. Using a t-distribution, calculate the 95% confidence interval for the true mean of daily latte sales using the data sample collected in Table 2. Table 2. Latte sales per day Latte sales (in cups) Date Day 1 104 Day 2 121 Day 3 110 Day 4 130 Day 5 122 Day 6 105 Day 7 Day 8 102 Day 9 111 ho What is the lower limit of this 95% confidence interval? Round to the nearest integer. What is the upper limit of this 95% confidence interval? Round to the nearest integer. Now, Ralph Henderson would like to check if the price change affected latte sales. The average number of lattes sold per day before the price changed was 92. His null hypothesis and alternative hypothesis are as follows: •HO: The current latte sales are not greater than before the price change. .HT: The current latte sales are greater than before the price change. Using a t-distribution and the information given in Table 2 above, calculate the p-value of the sample in Table 2 Round your answer with FOUR decimal places. Given the p-value, what could Ralph Henderson conclude using 99% confidence level? Choose the best answer He can reject HO. He can accept HO. He cannot reject HO. Fifteen days ago, Ralph Henderson started selling macaron boxes in his coffee shop to offer customers something sweet to have with their preferred beverage. After careful observation, he believes that sales of macaron boxes may be influenced by tea sales and weather. He decided to build a linear regression model with "macaron boxes sales as the dependent variable, and "weather" and "tea sales" as independent variables. Use the data provided in Table 3 to build this linear regression model. Note that weather is coded in a way that 0 represents a rainy day and 1 represents a sunny day. Table 3. Weather, tea sales, and macaron sales Weather Tea sales (in cups) Macaron sales (in boxes) 125 35 24 33 29 30 28 Day 101 1 Day 102 Day 103 1 Day 104 1 Day 105 o Day 106 o Day 107 1 Day 108 1 bay 109 Day 110 1 Day 111 b Day 112 b Day 113 1 Day 114 o Day 115 1 Day 116 1 92 106 109 106 M 106 127 123 106 120 110 102 130 1:30 135 33 p9 37 b1 44 140 41 30 49 60 How much of the variation in the total macaron sales can be explained by the two independent variables given on Table 3 without adjustment based on the number of independent variables? Enter your answer as a decimal number with four decimal places. E.g. If your asnwer is 73.89%, enter 0.7389 in the answer box. Which independent variables in this regression model are statistically significant at a 0.05 significance level? Choose at that apply. Weather Tea sales None of them were statistically significant Ralph Henderson owns a cafe near MIT. His cafe is always crowded with students who need caffeine to start their day. Ralph Henderson wants to serve the freshest coffee to his customers. He would like to understand his coffee sales better in order to roast the right amount of coffee beans every day. First, Ralph Henderson would like to explore the demand for pour-over coffee. He expects the daily demand for pour-over coffee to be stable at 130 cups per day. To test his hypothesis, he collected actual demand data for pour-over coffee for a week (see Table 1). Table 1. Actual demand and expected demand for pour-over coffee (in cups). actual demand expected demand 130 130 130 Monday 124 Tuesday 156 Wednesday 162 Thursday 129 nday 120 130 130 Run a chi-square test to compare actual and expected demand distributions. What is the p-value of your chi-square test? Round to FOUR decimal points Can Ralph state that the demand for pour-over coffee is significantly different from his expected distribution at 95% confidence? Choose the best answer The demand is significantly different from the expected distribution The demand is not significantly different from the expected distribution None of the above Ralph Henderson recently changed the price of a cup of latte. He would like to understand the latte sales better after the price change. Firstly, he decided to find out the confidence interval for daily latte sales after the price change. Using a t-distribution, calculate the 95% confidence interval for the true mean of daily latte sales using the data sample collected in Table 2. Table 2. Latte sales per day Latte sales (in cups) Date Day 1 104 Day 2 121 Day 3 110 Day 4 130 Day 5 122 Day 6 105 Day 7 Day 8 102 Day 9 111 ho What is the lower limit of this 95% confidence interval? Round to the nearest integer. What is the upper limit of this 95% confidence interval? Round to the nearest integer. Now, Ralph Henderson would like to check if the price change affected latte sales. The average number of lattes sold per day before the price changed was 92. His null hypothesis and alternative hypothesis are as follows: •HO: The current latte sales are not greater than before the price change. .HT: The current latte sales are greater than before the price change. Using a t-distribution and the information given in Table 2 above, calculate the p-value of the sample in Table 2 Round your answer with FOUR decimal places. Given the p-value, what could Ralph Henderson conclude using 99% confidence level? Choose the best answer He can reject HO. He can accept HO. He cannot reject HO. Fifteen days ago, Ralph Henderson started selling macaron boxes in his coffee shop to offer customers something sweet to have with their preferred beverage. After careful observation, he believes that sales of macaron boxes may be influenced by tea sales and weather. He decided to build a linear regression model with "macaron boxes sales as the dependent variable, and "weather" and "tea sales" as independent variables. Use the data provided in Table 3 to build this linear regression model. Note that weather is coded in a way that 0 represents a rainy day and 1 represents a sunny day. Table 3. Weather, tea sales, and macaron sales Weather Tea sales (in cups) Macaron sales (in boxes) 125 35 24 33 29 30 28 Day 101 1 Day 102 Day 103 1 Day 104 1 Day 105 o Day 106 o Day 107 1 Day 108 1 bay 109 Day 110 1 Day 111 b Day 112 b Day 113 1 Day 114 o Day 115 1 Day 116 1 92 106 109 106 M 106 127 123 106 120 110 102 130 1:30 135 33 p9 37 b1 44 140 41 30 49 60 How much of the variation in the total macaron sales can be explained by the two independent variables given on Table 3 without adjustment based on the number of independent variables? Enter your answer as a decimal number with four decimal places. E.g. If your asnwer is 73.89%, enter 0.7389 in the answer box. Which independent variables in this regression model are statistically significant at a 0.05 significance level? Choose at that apply. Weather Tea sales None of them were statistically significant

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